Publications | LIP6 - Équipe QI

Complexity of geometrically local stoquastic Hamiltonians

Wed, 11 Feb 2026 00:00:00 +0000

The QMA-completeness of the local Hamiltonian problem is a landmark result of the field of Hamiltonian complexity that studies the computational complexity of problems in quantum many-body physics. Since its proposal, substantial effort has been invested in better understanding the problem for physically motivated important families of Hamiltonians. In particular, the QMA-completeness of approximating the ground state energy of local Hamiltonians has been extended to the case where the Hamiltonians are geometrically local in one and two spatial dimensions. Among those physically motivated Hamiltonians, stoquastic Hamiltonians play a particularly crucial role, as they constitute the manifestly sign-free Hamiltonians in Monte Carlo approaches. Interestingly, for such Hamiltonians, the problem at hand becomes more ‘‘classical’’, being hard for the class MA (the randomized version of NP) and its complexity has tight connections with derandomization. In this work, we prove that both the two- and one-dimensional geometrically local analogues remain MA-hard with high enough qudit dimension. Moreover, we show that related problems are StoqMA-complete.

A unified framework for Bell inequalities from continuous-variable contextuality

Tue, 03 Feb 2026 00:00:00 +0000

Although the original EPR paradox was formulated in terms of position and momentum, most studies of these phenomena have focused on measurement scenarios with only a discrete number of possible measurement outcomes. Here, we present a framework for studying non-locality that is agnostic to the dimension of the physical systems involved, allowing us to probe purely continuous-variable, discrete-variable, or hybrid non-locality. Our approach allows us to find the optimal Bell inequality for any given measurement scenario and quantifies the amount of non-locality that is present in measurement statistics. This formalism unifies the existing literature on continuous-variable non-locality and allows us to identify new states in which Bell non-locality can be probed through homodyne detection. Notably, we find the first example of continuous-variable non-locality that cannot be mapped to a CHSH Bell inequality. Moreover, we provide several examples of simple hybrid DV-CV entangled states that could lead to near-term violation of Bell inequalities.

Quantum pseudoresources imply cryptography

Thu, 08 Jan 2026 00:00:00 +0000

While one-way functions (OWFs) serve as the minimal assumption for computational cryptography in the classical setting, in quantum cryptography, we have even weaker cryptographic assumptions such as pseudo-random states, and EFI pairs, among others. Moreover, the minimal assumption for computational quantum cryptography remains an open question. Recently, it has been shown that pseudoentanglement is necessary for the existence of quantum cryptography (Goulão and Elkouss 2024), but no cryptographic construction has been built from it. In this work, we study the cryptographic usefulness of quantum pseudoresources—a pair of families of quantum states that exhibit a gap in their resource content yet remain computationally indistinguishable. We show that quantum pseudoresources imply a variant of EFI pairs, which we call EPFI pairs, and that these are equivalent to quantum commitments and thus EFI pairs. Our results suggest that, just as randomness is fundamental to classical cryptography, quantum resources may play a similarly crucial role in the quantum setting. Finally, we focus on the specific case of entanglement, analyzing different definitions of pseudoentanglement and their implications for constructing EPFI pairs. Moreover, we propose a new cryptographic functionality that is intrinsically dependent on entanglement as a resource.

Quantum backreaction in an analog black hole

Tue, 23 Dec 2025 00:00:00 +0000

Backreaction equations for 1 + 1 dimensional BEC sonic black holes

Mon, 15 Dec 2025 00:00:00 +0000

We present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two-dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons, hybrid light-matter quasiparticles, and measure both phase and modulus of the order parameter in the turbulent regime. Fundamental topological conservation laws require that the formation and annihilation of vortices also involve critical points of the velocity field, namely nodes and saddles. Identifying the simplest mechanisms underlying these processes enables us to develop an effective kinetic model that closely aligns with the experimental observations, and shows that different processes are responsible for vortex number growth and decay. These findings underscore the crucial role played by topological constraints in shaping nonlinear, turbulent evolution of two-dimensional quantum fluids.

Higher-order quantum computing with known input states

Mon, 15 Dec 2025 00:00:00 +0000

88 pages, 27 figures. A concise overview of the main results is provided in the Sec. 2 (Summary of main results) for a quick read

Exponential separation in quantum query complexity of the quantum switch with respect to simulations with standard quantum circuits

Wed, 10 Dec 2025 00:00:00 +0000

Quantum theory is consistent with a computational model permitting black-box operations to be applied in an indefinite causal order, going beyond the standard circuit model of computation. The quantum switch – the simplest such example – has been shown to provide numerous information-processing advantages. Here, we prove that the action of the quantum switch on two $n$-qubit quantum channels cannot be simulated deterministically and exactly by any causally ordered quantum circuit that uses $M$ calls to one channel and one call to the other, if $M \leq \max(2, 2^n-1)$. This demonstrates an exponential separation in quantum query complexity of indefinite causal order compared to standard quantum circuits.

Orbit dimensions in linear and Gaussian quantum optics

Wed, 10 Dec 2025 00:00:00 +0000

Added details on homodyne measurements approach, and fixed typos

Analysis of untrusted-node quantum key distribution from a geostationary satellite

Tue, 09 Dec 2025 00:00:00 +0000

In pursuit of a global quantum key distribution (QKD) network, a service based on untrusted nodes on geostationary satellites could offer wide coverage, continuous operation, and enhanced security compared to the trusted node alternative. Although this scenario has been studied for entanglement-based protocols, such an approach would require large-area telescopes both on the ground and in space. In this work, we analyze the performance of two QKD protocols well adapted to this scenario, namely twin-field (TF) and mode-pairing (MP) QKD, which exhibit high resilience to high-loss channels. Leveraging an in-depth simulation of communication channels corrected with adaptive optics, we assess the expected secret key rates for both protocols in a configuration involving two 50 cm telescopes on board the satellite and ground-based telescopes ranging from 20 cm to 1 m in aperture. Our results show that, in the best case and considering realistic detectors, it is possible to achieve secret key rates on the order of a few hundred bit/s for both TF and MP-QKD. We show, notably, that secret key generation is potentially feasible even with 20 cm ground telescopes, highlighting the high scalability potential of such a configuration.

Continuous-variable quantum communication

Tue, 09 Dec 2025 00:00:00 +0000

Tremendous progress in experimental quantum optics during the past decades enabled the advent of quantum technologies, one of which is quantum communication. Aimed at novel methods for more secure or efficient information transfer, quantum communication has developed into an active field of research and proceeds toward full-scale implementations and industrialization. Continuous-variable methods of multi-photon quantum state preparation, manipulation, and coherent detection, as well as the respective theoretical tools of phase-space quantum optics, offer the possibility to make quantum communication efficient, applicable and accessible, thus boosting the development of the field. We review the methodology, techniques and protocols of continuous-variable quantum communication, from the first theoretical ideas, through milestone implementations, to the recent developments, covering quantum key distribution as well as other quantum communication schemes, suggested on the basis of continuous-variable states and measurements.

Efficient Gate Reordering for Distributed Quantum Compiling in Data Centers

Tue, 09 Dec 2025 00:00:00 +0000

Just as classical computing relies on distributed systems, the quantum computing era requires new kinds of infrastructure and software tools. Quantum networks will become the backbone of hybrid, quantum-augmented data centers, in which quantum algorithms are distributed over a local network of quantum processing units (QPUs) interconnected via shared entanglement. In this context, it is crucial to develop methods and software that minimize the number of inter-QPU communications. Here we describe key features of the quantum compiler araQne, which is designed to minimize distribution cost, measured by the number of entangled pairs required to distribute a monolithic quantum circuit using gate teleportation protocols. We establish the crucial role played by circuit reordering strategies, which strongly reduce the distribution cost compared to a baseline approach.

Experimental Quantum Electronic Voting

Tue, 09 Dec 2025 00:00:00 +0000

Quantum information protocols offer significant advantages in properties such as security, anonymity, and privacy for communication and computing tasks. An application where guaranteeing the highest possible security and privacy is critical for democratic societies is electronic voting. As computational power continues to evolve, classical voting schemes may become increasingly vulnerable to information leakage. In this work, we present the experimental demonstration of an information-theoretically secure and efficient electronic voting protocol that, crucially, does not rely on election authorities, leveraging the unique properties of quantum states. Our experiment is based on a high-performance source of Greenberger-Horne-Zeilinger (GHZ) states and realizes a proof-of-principle implementation of the protocol in two scenarios: a configuration with four voters and two candidates employing privacy enhancement techniques and an election scenario supporting up to eight voters and sixteen candidates. The latter is particularly well-suited for secure board-level elections within organizations or small-scale governmental contexts.

Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints

Tue, 09 Dec 2025 00:00:00 +0000

Understanding the connections between different quantum information protocols has been proven fruitful for both theoretical insights and experimental applications. In this work, we explore the relationship between non-local and prepare-and-measure scenarios, proposing a systematic way to translate bipartite Bell inequalities into dimensionally-bounded prepare-and-measure tasks. We identify sufficient conditions under which the translation preserves the quantum bound and self-testing properties, enabling a wide range of certification protocols originally developed for the non-local setting to be adapted to the sequential framework of prepare-and-measure with a dimensional bound. While the dimensionality bound is not device-independent, it still is a practical and experimentally reasonable assumption in many cases of interest. In some instances, we find new experimentally-friendly certification protocols. In others, we demonstrate equivalences with already known prepare-and-measure protocols, where self-testing results were previously established using alternative mathematical methods. Our results unify different quantum correlation frameworks, and contribute to the ongoing research effort of studying the interplay between parallel and sequential protocols.

Computational Monogamy of Entanglement and Non-interactive Quantum Key Distribution

Mon, 01 Dec 2025 00:00:00 +0000

Quantum key distribution (QKD) enables Alice and Bob to exchange a secret key over a public, untrusted quantum channel. Compared to classical key exchange, QKD achieves everlasting security: after the protocol execution the key is secure against adversaries that can do unbounded computations. On the flip side, while classical key exchange can be achieved non-interactively (with two simultaneous messages between Alice and Bob), no non-interactive protocol is known that provides everlasting security, even using quantum information.

A unifying account of warm start guarantees for patches of quantum landscapes

Fri, 28 Nov 2025 00:00:00 +0000

Barren plateaus are fundamentally a statement about quantum loss landscapes on average but there can, and generally will, exist patches of barren plateau landscapes with substantial gradients. Previous work has studied certain classes of parameterized quantum circuits and found example regions where gradients vanish at worst polynomially in system size. Here we present a general bound that unifies all these previous cases and that can tackle physically-motivated ansätze that could not be analyzed previously. Concretely, we analytically prove a lower-bound on the variance of the loss that can be used to show that in a non-exponentially narrow region around a point with curvature the loss variance cannot decay exponentially fast. This result is complemented by numerics and an upper-bound that suggest that any loss function with a barren plateau will have exponentially vanishing gradients in any constant radius subregion. Our work thus suggests that while there are hopes to be able to warm-start variational quantum algorithms, any initialization strategy that cannot get increasingly close to the region of attraction with increasing problem size is likely inadequate.

Catalytic Activation of Bell Nonlocality

Tue, 25 Nov 2025 00:00:00 +0000

The correlations of certain entangled states can be perfectly simulated classically via a local model. Hence such states are termed Bell local, as they cannot lead to Bell inequality violation. Here, we show that Bell nonlocality can nevertheless be activated for certain Bell-local states via a catalytic process. Specifically, we present a protocol where a Bell-local state, combined with a catalyst, is transformed into a Bell-nonlocal state while the catalyst is returned exactly in its initial state. Importantly, this transformation is deterministic and based only on local operations. Moreover, this procedure is possible even when the state of the catalyst is itself Bell local, demonstrating a new form of superactivation of Bell nonlocality, as well as an interesting form of quantum catalysis. On the technical level, our main tool is a formal connection between catalytic activation and many-copy activation, which is of independent interest.

Simulating the quantum switch with quantum circuits is computationally hard

Thu, 20 Nov 2025 00:00:00 +0000

Higher-order transformations acting on input quantum channels in an indefinite causal order—such as the quantum switch—cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is whether they can be simulated, i.e., whether their action can be exactly and deterministically reproduced by a quantum circuit with more calls to the input channels. Here, we prove that the quantum switch acting on two n-qubit channels cannot be simulated by any quantum circuit using k calls to one channel and one to the other, if k < 2^n. This establishes an exponential separation in quantum query complexity between processes with indefinite causal order and quantum circuits. Moreover, even with one extra call to both input channels, such a simulation remains impossible. We further demonstrate the robustness of this separation by extending the result to probabilistic and approximate simulations scenarios.

Violating Bell inequalities using photon path encoding

Wed, 12 Nov 2025 00:00:00 +0000

In this work we investigate the use of photon path entanglement for the violation of a Bell inequality. The advantage of this encoding is that Bell pairs can be distributed with a rate scaling as the square root of the transmitivity of the channel in an heralding protocol, instead of a linear scaling in e.g. polarisation-based schemes. The drawback is that it is hard to implement generic Pauli measurements. We explore different ways to implement tackle this issue.

Quantum bounds for compiled XOR games and $d$-outcome CHSH games

Tue, 28 Oct 2025 00:00:00 +0000

Nonlocal games play a crucial role in quantum information theory and have numerous applications in certification and cryptographic protocols. Kalai et al. (STOC 2023) introduced a procedure to compile a nonlocal game into a single-prover interactive proof, using a quantum homomorphic encryption scheme, and showed that their compilation method preserves the classical bound of the game. Natarajan and Zhang (FOCS 2023) then showed that the quantum bound is preserved for the specific case of the CHSH game. Extending the proof techniques of Natarajan and Zhang, we show that the compilation procedure of Kalai et al. preserves the quantum bound for two classes of games: XOR games and d-outcome CHSH games. We also establish that, for any pair of qubit measurements, there exists an XOR game such that its optimal winning probability serves as a self-test for that particular pair of measurements.

The power of quantum catalytic local operations

Mon, 13 Oct 2025 00:00:00 +0000

A key result in entanglement theory is that the addition of a catalyst dramatically enlarges the set of possible state transformations via local operations and classical communication (LOCC). However, it remains unclear what is the interplay between classical communication and quantum catalysis. Here our aim is to disentangle the effect of the catalyst from that of classical communication. To do so, we explore a class of state transformations termed catalytic local operations (CLO) and compare it to LOCC and to stochastic LOCC augmented by bounded quantum communication. We show that these classes are incomparable and capture different facets of quantum state transformations.

Out-of-Distribution Generalization for Learning Quantum Channels with Low-Energy Coherent States

Wed, 08 Oct 2025 00:00:00 +0000

When experimentally learning the action of a continuous-variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is to use low-energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low-energy inputs but very differently for high-energy inputs. They may also act similarly on coherent-state inputs but differently on nonclassical inputs. Extrapolating the behavior of a channel for more general input states from its action on the far more limited set of low-energy coherent states is a case of out-of-distribution generalization. To be sure that such generalization gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low-energy coherent-state inputs, one can bound how different the input-output relations are for any (high-energy or highly nonclassical) input. This proves that out-of-distribution generalization is always possible for learning quantum channels using low-energy coherent states, as long as enough samples are used.

Efficient Quantum Measurements: Computational Max-and Measured Rényi Divergences and Applications

Wed, 01 Oct 2025 00:00:00 +0000

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational constraints. Using geometric, computational, and information theoretic tools, we define two new types of computational divergences, which we term computational max-divergence and computational measured Rényi divergences. Both are constrained by a family of efficient binary measurements, and thus useful for state discrimination tasks in the computational setting. We prove that, in the infinite-order limit, the computational measured Rényi divergence coincides with the computational max-divergence, mirroring the corresponding relation in the unconstrained information-theoretic setting. For the many-copy regime, we introduce regularized versions and establish a one-sided computational Stein bound on achievable hypothesis-testing exponents under efficient measurements, giving the regularized computational measured relative entropy an operational meaning. We further define resource measures induced by our computational divergences and prove an asymptotic continuity bound for the computational measured relative entropy of resource. Focusing on entanglement, we relate our results to previously proposed computational entanglement measures and provide explicit separations from the information-theoretic setting. Together, these results provide a principled, cohesive approach towards state discrimination tasks and resource quantification under computational constraints.

Post-Quantum Zero-Knowledge with Space-Bounded Simulation

Wed, 01 Oct 2025 00:00:00 +0000

The Role of Piracy in Quantum Proofs

Wed, 01 Oct 2025 00:00:00 +0000

A well-known feature of quantum information is that it cannot, in general, be cloned. Recently, a number of quantum-enabled information-processing tasks have demonstrated various forms of uncloneability; among these forms, piracy is an adversarial model that gives maximal power to the adversary in controlling both a cloning-type attack, as well as the evaluation/verification stage. Here, we initiate the study of anti-piracy proof systems, which are proof systems that inherently prevent piracy attacks. We define anti-piracy proof systems, demonstrate such a proof system for an oracle problem, and also describe a candidate anti-piracy proof system for {$}{$}{\backslash}textsf {{}NP {}} {$}{$}NP. We also study quantum proof systems that are cloneable and settle the famous QMA vs. {$}{$}{\backslash}textsf {{}QMA {}} (2){$}{$}QMA(2)debate in this setting. Lastly, we discuss how one can approach the QMA vs. QCMA question, by studying its cloneable variants.

Quantum cryptography integrating an optical quantum memory

Fri, 19 Sep 2025 00:00:00 +0000

Developments in scalable quantum networks rely critically on optical quantum memories, which are key components enabling the storage of quantum information. These memories play a pivotal role for entanglement distribution and long-distance quantum communication, with remarkable advances achieved in this context. However, optical memories have broader applications, and their storage and buffering capabilities can benefit a wide range of future quantum technologies. Here we present the first demonstration of a cryptography protocol incorporating an intermediate quantum memory layer. Specifically, we implement Wiesner’s unforgeable quantum money primitive with a storage step, rather than as an on-the-fly procedure. This protocol imposes stringent requirements on storage efficiency and noise level to reach a secure regime. We demonstrate the implementation with polarization encoding of weak coherent states of light and a high-efficiency cold-atom-based quantum memory, and validate the full scheme. Our results showcase a major capability, opening new avenues for quantum memory utilization and network functionalities.

Dynamic Scheduling in Fiber and Spaceborne Quantum Repeater Networks

Thu, 18 Sep 2025 00:00:00 +0000

In this thesis, we analyze the problem of scheduling in the context of quantum networks. Given a quantum network, the scheduling problem amounts to choosing which entanglement swapping operations to perform to better serve user demand. The choice can be carried out following a variety of criteria (e.g. ensuring all users are served equally vs. prioritizing specific critical applications, properly managing load spikes and node failures, adopting heuristic or optimization-based algorithms…), warranting the need for a method to compare different solutions and choose the most appropriate. We present here a framework to mathematically formulate the scheduling problem over quantum networks and benchmark possible solutions in a variety of environments. Our framework enables the benchmarking of general quantum scheduling policies over arbitrary lossy multicommodity quantum networks. By leveraging the framework, we apply Lyapunov drift minimization (a standard technique in classical network science) to derive a novel class of quadratic optimization based scheduling policies, which we then analyze and compare with a simpler, Max Weight inspired linear class to quantify the performance loss due to the simplification. We start our second chapter with an overview of the pre-existing fiber quantum simulation tools. The rest of the chapter is devoted to the development of numerous extensions to QuISP, an established quantum network simulator focused on scalability and accuracy in modeling the classical communication infrastructure underlying every quantum network. We document the development of our extensions allowing to simulate satellite links and multiple connections in QuISP, with an account of the currently functional extensions (free-space links and connection teardown) and of the ones still under active development (network multiplexing). Since it is likely that a future global-scale quantum network will incorporate satellite interconnections, we devote a chapter to the study of quantum satellite links. We derive an analytical model for the entanglement distribution rates for satellite-to-ground and ground-satellite-ground links and discuss different quantum memory allocation policies for the dual link case. Our findings show that classical communication latency is a major limiting factor for satellite communication, and the effects of physical upper bounds such as the speed of light must be taken into account when designing quantum links, limiting the attainable rates to tens of kHz. We also investigate the issue of differential latency, a Doppler-like effect caused by the displacement of satellite nodes that changes the timing of incoming photons and adds another upper bound to the generation rate. We conclude the thesis by summarizing our findings and highlighting the challenges that still need to be overcome in order to study the quantum scheduling problem over fiber and satellite large scale quantum networks.

Formalizing contextuality in sequential scenarios

Thu, 18 Sep 2025 00:00:00 +0000

This paper provides a framework for characterizing sequential scenarios, allowing for the identification of contextuality given empirical data, and then provides precise operational interpretations in terms of the possible hidden variable model explanations of that data. Sequential scenarios are different in essence from non-local scenarios as each measurement instrument is allowed to change the state as it enters subsequent measurement instruments. Thus, it is necessary to formulate the possible state update in any hidden variable model description. Here we develop such hidden variable models for sequential scenarios, and we propose the notion of no-disturbance: an instrument A does not disturb another instrument B if the statistics of B are independent of whether A was measured or not. We define non-contextuality inequalities for the sequential scenario, and show that violation implies that the data cannot be explained by a hidden variable model that is both deterministic and not disturbing in this sense. We further provide a translation from standard contextuality frameworks to ours, providing sequential versions which carry over the same inequalities and measures of contextuality, but now with the sequential interpretations stated.

Privacy in continuous-variable distributed quantum sensing

Wed, 17 Sep 2025 00:00:00 +0000

Can a distributed network of quantum sensors estimate a global parameter while protecting every locally encoded value? We answer this question affirmatively by introducing and analysing a protocol for distributed quantum sensing in the continuous-variable regime. We consider a multipartite network in which each node encodes a local phase into a shared entangled Gaussian state. We show that the average phase can be estimated with high precision, exhibiting Heisenberg scaling in the total photon number, while individual phases are inaccessible. Although complete privacy - where all other combinations of phases remain entirely hidden - is unattainable for finite squeezing in multi-party settings, it emerges in the large-squeezing limit. We further investigate the impact of displacements and optical losses, revealing trade-offs between estimation accuracy and privacy. Finally, we benchmark the protocol against other continuous-variable resource states.

Robustly self-testing all maximally entangled states in every finite dimension

Tue, 16 Sep 2025 00:00:00 +0000

We establish a device-independent, noise-tolerant certification of maximally entangled states in every finite dimension $d$. The core ingredient is a $d$-input, $d$-outcome Bell experiment that generalizes the Clauser-Horne-Shimony-Holt test from qubits to qudits, where each setting is a non-diagonal Heisenberg-Weyl observable. For every odd prime $d \geq 3$, the associated Bell operator has an exact sum-of-positive-operators decomposition, yielding the Cirelson bound in closed form, from which we reconstruct the Heisenberg-Weyl commutation relations on the support of the state. We then extend the Mayers-Yao local isometry from qubits to prime-dimensional systems and show that any $ε$-near-optimal strategy below that bound is, up to local isometries, within trace distance $δ= \mathcal{O}(\sqrtε)$ of the ideal maximally entangled state; the implemented measurements are correspondingly close to the target observables. Via a tensor-factor argument, the prime-dimension result extends the self-testing protocol to every composite dimension $d$. The protocol uses standard Heisenberg-Weyl operations and non-Clifford phase gates that are diagonal in the computational basis, making it directly applicable to high-dimensional photonic and atomic platforms.

StoqMA vs. MA: the power of error reduction

Thu, 11 Sep 2025 00:00:00 +0000

StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as BPP, BQP, MA, QMA, etc.,this property remains open for StoqMA since Bravyi, Bessen and Terhal defined this class in 2006. In this note, we show that error reduction forStoqMA will imply that StoqMA = MA.

Strict hierarchy between $n$-wise measurement simulability, compatibility structures, and multi-copy compatibility

Thu, 04 Sep 2025 00:00:00 +0000

The incompatibility of quantum measurements, i.e. the fact that certain observable quantities cannot be measured jointly is widely regarded as a distinctive quantum feature with important implications for the foundations and the applications of quantum information theory. While the standard incompatibility of multiple measurements has been the focus of attention since the inception of quantum theory, its generalizations, such as measurement simulability, $n$-wise incompatibility, and mulit-copy incompatibility have only been proposed recently. Here, we point out that all these generalizations are differing notions of the question of how many measurements are genuinely contained in a measurement device. We then show, that all notions do differ not only in their operational meaning but also mathematically in the set of measurement assemblages they describe. We then fully resolve the relations between these different generalizations, by showing a strict hierarchy between these notions. Hence, we provide a general framework for generalized measurement incompatibility. Finally, we consider the implications our results have for recent works using these different notions.

Structured-Seed Local Pseudorandom Generators and Their Applications

Mon, 11 Aug 2025 00:00:00 +0000

We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a generic template for constructing SSL-PRGs that combines the following two ingredients: [i.] 1) noisy‑NC⁰ PRGs, computable by constant‑depth circuits fed with sparse noise, with 2) new local compression schemes for sparse vectors derived from combinatorial batch codes. Instantiating the template under the sparse Learning‑Parity‑with‑Noise (LPN) assumption yields the first SSL-PRGs with polynomial stretch and constant locality from a subquadratic‑sample search hardness assumption; a mild strengthening of sparse‑LPN gives strong SSL-PRGs of arbitrary polynomial stretch. We further show that for all standard noise distributions, noisy‑local PRGs cannot be emulated by ordinary local PRGs, thereby separating the two notions. Plugging SSL-PRGs into existing frameworks, we revisit the canonical applications of local PRGs and demonstrate that SSL-PRGs suffice for: (i) indistinguishability obfuscation, (ii) constant-overhead secure computation, (iii) compact homomorphic secret sharing, and (iv) deriving hardness results for PAC‑learning DNFs from sparse‑LPN. Our work thus broadens the landscape of low‑depth pseudorandomness and anchors several primitives to a common, well‑motivated assumption.

Toward quantum advantage with photonic state injection

Fri, 11 Jul 2025 00:00:00 +0000

We propose a new scheme for near-term photonic quantum devices that allows us to increase the expressive power of the quantum models beyond what linear optics can do. This scheme relies upon state injection, a measurement-based technique that can produce states that are more controllable, and solve learning tasks that are believed to be intractable classically. We explain how circuits made of linear optical architectures separated by state injections are well-suited for experimental implementation. In addition, we give theoretical results regarding the evolution of the purity of the resulting states, and we discuss how it impacts the distinguishability of the circuit outputs. Finally, we study a computational subroutine of learning algorithms named probability estimation, and we show that the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved than state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that rely on overcoming fewer experimental difficulties.

A complexity transition in displaced Gaussian Boson sampling

Wed, 09 Jul 2025 00:00:00 +0000

Abstract Gaussian Boson Sampling (GBS) is the problem of sampling from the output of photon-number-resolving measurements of squeezed states input to a linear optical interferometer. For purposes of demonstrating quantum computational advantage as well as practical applications, a large photon number is often desirable. However, producing squeezed states with high photon numbers is experimentally challenging. In this work, we examine the computational complexity implications of increasing the photon number by introducing coherent states. This displaces the state in phase space and as such we call this modified problem Displaced GBS . By utilising a connection to the matching polynomial in graph theory, we first describe an efficient classical algorithm for Displaced GBS when displacement is high or when the output state is represented by a non-negative graph. Then we provide complexity theoretic arguments for the quantum advantage of the problem in the low-displacement regime and numerically quantify where the complexity transition occurs.

A complexity theory for non-local quantum computation

Tue, 03 Jun 2025 00:00:00 +0000

Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a characterization of entanglement cost in at least certain NLQC tasks would imply significant breakthroughs in complexity theory. Here, we avoid these obstructions and take an indirect approach to understanding resource requirements in NLQC, which mimics the approach used by complexity theorists: we study the relative hardness of different NLQC tasks by identifying resource efficient reductions between them. Most significantly, we prove that $f$-measure and $f$-route, the two best studied NLQC tasks, are in fact equivalent under $O(1)$ overhead reductions. This result simplifies many existing proofs in the literature and extends several new properties to $f$-measure. For instance, we obtain sub-exponential upper bounds on $f$-measure for all functions, and efficient protocols for functions in the complexity class $\mathsf{Mod}_k\mathsf{L}$. Beyond this, we study a number of other examples of NLQC tasks and their relationships.

Cryptography from Lossy Reductions: Towards OWFs from ETH, and Beyond

Fri, 30 May 2025 00:00:00 +0000

One-way functions (OWFs) form the foundation of modern cryptography, yet their unconditional existence remains a major open question. In this work, we study this question by exploring its relation to lossy reductions, i.e., reductions~$R$ for which it holds that $I(X;R(X)) \ll n$ for all distributions~$X$ over inputs of size $n$. Our main result is that either OWFs exist or any lossy reduction for any promise problem~$\Pi$ runs in time~$2^{\Omega(\log\tau_\Pi / \log\log n)}$, where $\tau_\Pi(n)$ is the infimum of the runtime of all (worst-case) solvers of~$\Pi$ on instances of size~$n$. In fact, our result requires a milder condition, that $R$ is lossy for sparse uniform distributions (which we call mild-lossiness). It also extends to $f$-reductions as long as $f$ is a non-constant permutation-invariant Boolean function, which includes And-, Or-, Maj-, Parity-, Modulo $k$, and Threshold $k$-reductions. Additionally, we show that worst-case to average-case Karp reductions and randomized encodings are special cases of mildly-lossy reductions and improve the runtime above as $2^{\Omega(\log \tau_\Pi)}$ when these mappings are considered. Restricting to weak fine-grained OWFs, this runtime can be further improved as~$\Omega(\tau_\Pi)$. Taking~$\Pi$ as~$kSAT$, our results provide sufficient conditions under which (fine-grained) OWFs exist assuming the Exponential Time Hypothesis (ETH). Conversely, if (fine-grained) OWFs do not exist, we obtain impossibilities on instance compressions (Harnik and Naor, FOCS 2006) and instance randomizations of~$kSAT$ under the ETH. Finally, we partially extend these findings to the quantum setting; the existence of a pure quantum mildly-lossy reduction for $\Pi$ within the runtime~$2^{o(\log\tau_\Pi / \log\log n)}$ implies the existence of one-way state generators.

All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality

Wed, 21 May 2025 00:00:00 +0000

Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multi-particle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning

Thu, 15 May 2025 00:00:00 +0000

Quantum machine learning (QML) has become a promising area for real world applications of quantum computers, but near-term methods and their scalability are still important research topics. In this context, we analyze the trainability and controllability of specific Hamming weight preserving variational quantum circuits (VQCs). These circuits use qubit gates that preserve subspaces of the Hilbert space, spanned by basis states with fixed Hamming weight k . In this work, we first design and prove the feasibility of new heuristic data loaders, performing quantum amplitude encoding of ( n k ) -dimensional vectors by training an n -qubit quantum circuit. These data loaders are obtained using controllability arguments, by checking the Quantum Fisher Information Matrix (QFIM)’s rank. Second, we provide a theoretical justification for the fact that the rank of the QFIM of any VQC state is almost-everywhere constant, which is of separate interest. Lastly, we analyze the trainability of Hamming weight preserving circuits, and show that the variance of the l 2 cost function gradient is bounded according to the dimension ( n k ) of the subspace. This proves conditions of existence/lack of Barren Plateaus for these circuits, and highlights a setting where a recent conjecture on the link between controllability and trainability of variational quantum circuits does not apply.

Quantum machine learning on near term hardware with unstructured and graph structured data

Mon, 12 May 2025 00:00:00 +0000

Machine learning enabled the resolution of many real world problems that other traditional computational method struggled to solve, or could solve in more expensive ways. Quantum computing is a paradigm of computation using the quantum states of matter that enables a large computational speed up on some problems. The recent progress in the development of quantum hardware encouraged the research of concrete applications of quantum computers. It then became natural to look for ways in which quantum computers can be applied for machine learning. This thesis is a contribution towards this goal. The first part aims at understanding the general capabilities of variational quantum circuits (VQC) for machine learning tasks given vector data inputs, and have a clearer idea on the necessary conditions in order to expect a quantum advantage. VQCs are a family of quantum algorithms where one finds gates parameters that minimizes a cost function, in the same way as neural networks. They are effectively linear models in a high dimensional feature space. I show that although VQCs are costly to evaluate, one can sometimes construct cheap classical approximators called classical surrogate using the technique of random features regression. If this approximation is possible, the quantum advantage is limited. I also highlight the fact that learning a classical model on the same feature map will lead to a solution called the Minimum Norm Least Square (MNLS) estimator, but the training dynamics of the quantum circuits will not necessarily lead to the same solution. This separation is the source of quantum advantage, I show that it is sufficient that the weight vector of quantum models has a large norm, and I give concrete examples. The second part explores the use of quantum computers to perform machine learning tasks on graph structured data. Machine learning on graph data encompasses many real world applications, and algorithms for vector data cannot be directly applied. I aimed in this part to develop quantum algorithms adapted to the graph structure of the data. The main idea is to encode the graph into a Hamiltonian that has the same topology. One then prepares a quantum state by evolving this Hamiltonian, and the measurements are incorporated in a classical machine learning algorithm. This approach is especially suited to neutral atoms quantum computers. With such platforms, one can indeed easily create a quantum system with the desired connectivity, and the geometry can be changed at each run. I developed a large family of algorithms, inspired by kernels, graphs neural networks, and transformers with the intention to be ran on current hardware. I performed numerical experiments on large scale datasets, and described the results of an experimental implementation on the hardware of Pasqal.

Security of a secret sharing protocol on the Qline

Tue, 29 Apr 2025 00:00:00 +0000

Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol. While traditional Quantum Key Distribution (QKD) can maintain security, its widespread deployment in general networks would incur prohibitive costs. In this work, we present a quantum protocol for distributing additive secret sharing of 0, which we prove to be composably secure within the Abstract Cryptography framework. Moreover, our protocol targets the Qline, a recently proposed quantum network architecture designed to simplify and reduce the cost of quantum communication. Once the shares are distributed, they can be used to securely perform a wide range of cryptographic tasks, including standard additive secret sharing, anonymous veto, and symmetric key establishment.

Quantum Key Distribution with Efficient Post-Quantum Cryptography-Secured Trusted Node on a Quantum Network

Wed, 23 Apr 2025 00:00:00 +0000

Quantum Key Distribution (QKD) enables two distant users to exchange a secret key with information-theoretic security, based on the fundamental laws of quantum physics. While it is arguably the most mature application of quantum cryptography, it has inherent limitations in the achievable distance and the scalability to large-scale infrastructures. While the applicability of QKD can be readily increased with the use of intermediary trusted nodes, this adds additional privacy requirements on third parties. In this work, we present an efficient scheme leveraging a trusted node with lower privacy requirements thanks to the use of post-quantum cryptographic techniques, and implement it on a deployed fiber optic quantum communication network in the Paris area.

Quantum pseudoresources imply cryptography

Tue, 22 Apr 2025 00:00:00 +0000

While one-way functions (OWFs) serve as the minimal assumption for computational cryptography in the classical setting, in quantum cryptography, we have even weaker cryptographic assumptions such as pseudo-random states, and EFI pairs, among others. Moreover, the minimal assumption for computational quantum cryptography remains an open question. Recently, it has been shown that pseudoentanglement is necessary for the existence of quantum cryptography (Goul~ao and Elkouss 2024), but no cryptographic construction has been built from it. In this work, we study the cryptographic usefulness of quantum pseudoresources – a pair of families of quantum states that exhibit a gap in their resource content yet remain computationally indistinguishable. We show that quantum pseudoresources imply a variant of EFI pairs, which we call EPFI pairs, and that these are equivalent to quantum commitments and thus EFI pairs. Our results suggest that, just as randomness is fundamental to classical cryptography, quantum resources may play a similarly crucial role in the quantum setting. Finally, we focus on the specific case of entanglement, analyzing different definitions of pseudoentanglement and their implications for constructing EPFI pairs. Moreover, we propose a new cryptographic functionality that is intrinsically dependent on entanglement as a resource.

Experimental Fiber-Based Quantum Triangle-Network Nonlocality with a Telecom Al Ga As Multiplexed Entangled-Photon Source

Mon, 21 Apr 2025 00:00:00 +0000

The exploration of the concept of nonlocality beyond standard Bell scenarios in quantum network architectures unveils fundamentally new forms of correlations that hold a strong potential for future applications of quantum communication networks. To materialize this potential, it is necessary to adapt theoretical advances to realistic configurations. Here, we consider a quantum triangle network, for which is has been shown in theory that, remarkably, quantum nonlocality without inputs can be demonstrated for sources with an arbitrarily small level of independence. We realize such correlated sources experimentally by carefully engineering the output state of a single Al Ga As multiplexed entangled-photon source, exploiting energy-matched channels cut in its broad spectrum. This simulated triangle network, based on standard fiber telecom components, is then used to violate experimentally a Bell-like inequality that we derive to capture the effect of noise in the correlations present in our system. We also rigorously validate our findings by analyzing the mutual information between the generated states. Our results allow us to deepen our understanding of network nonlocality while also pushing its practical relevance for quantum communication networks.

Experimental Fiber-Based Quantum Triangle-Network Nonlocality with a Telecom Al Ga As Multiplexed Entangled-Photon Source

Mon, 21 Apr 2025 00:00:00 +0000

Non-Interactive and Non-Destructive Zero-Knowledge Proofs on Quantum States and Multi-Party Generation of Authorized Hidden GHZ States

Fri, 11 Apr 2025 00:00:00 +0000

We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier).In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [Cojocaru et al. 2019; Gheorghiu and Vidick 2019] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubit state from a single superposition.Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.

The Round Complexity of Proofs in the Bounded Quantum Storage Model

Tue, 08 Apr 2025 00:00:00 +0000

The round complexity of interactive proof systems is a key question of practical and theoretical relevance in complexity theory and cryptography. Moreover, results such as QIP = QIP(3) (STOC'00) show that quantum resources significantly help in such a task. In this work, we initiate the study of round compression of protocols in the bounded quantum storage model (BQSM). In this model, the malicious parties have a bounded quantum memory and they cannot store the all the qubits that are transmitted in the protocol. Our main results in this setting are the following: 1. There is a non-interactive (statistical) witness indistinguishable proof for any language in NP (and even QMA) in BQSM in the plain model. We notice that in this protocol, only the memory of the verifier is bounded. 2. Any classical proof system can be compressed in a two-message quantum proof system in BQSM. Moreover, if the original proof system is zero-knowledge, the quantum protocol is zero-knowledge too. In this result, we assume that the prover has bounded memory. Finally, we give evidence towards the “tightness” of our results. First, we show that NIZK in the plain model against BQS adversaries is unlikely with standard techniques. Second, we prove that without the BQS model there is no 2–message zero-knowledge quantum interactive proof, even under computational assumptions.

Implementation of Protocols for Quantum Photonic Networks

Thu, 27 Mar 2025 00:00:00 +0000

This thesis is situated in the field of quantum information, with a particular focus on quantum communication networks. The goal of such networks is to enable fundamentally new technologies by facilitating quantum communication between distant parties, eventually leading to a Quantum Internet. These networks allow the transmission of quantum bits (qubits) over long distances, enabling tasks that are provably impossible for any classical communication network. Furthermore, the ability to generate entanglement between remote sites provides a powerful platform for fundamental studies of nature. Photonic resources are central to quantum network infrastructure, as they provide the optimal means for communication between the network nodes. In this thesis, we implement a photonic platform design capable of generating high-fidelity Greenberger-Horne-Zeilinger (GHZ) states at telecom wavelengths in a compact and scalable configuration. Our source relies on spontaneous parametric down-conversion within a layered Sagnac interferometer, requiring only a single nonlinear crystal. This design enables the generation of highly indistinguishable photon pairs, leading to high-quality multipartite entangled states. Using this source, we provide the first experimental demonstration of device-independent quantum state certification in the non-IID regime. This task is a fundamental building block for quantum communication and computation, as it determines whether the involved parties can trust their resources or whether the application should be aborted. We further investigate the sample efficiency of this protocol and analyze how it can be leveraged for robust and reliable quantum information processing. Additionally, we explore the privacy of individual parties in a distributed quantum sensing protocol by certifying the entangled states shared within the network.

A classical proof of quantum knowledge for multi-prover interactive proof systems

Thu, 20 Mar 2025 00:00:00 +0000

In a proof of knowledge (PoK), a verifier becomes convinced that a prover possesses privileged information. In combination with zero-knowledge proof systems, PoKs are an important part of secure protocols such as digital signature schemes and authentication schemes as they enable a prover to demonstrate possession of a certain piece of information (such as a private key or a credential), without revealing it. Formally, A PoK is defined via the existence of an extractor, which is capable of reconstructing the key information that makes a verifier accept, given oracle access to the prover. We extend the concept of a PoK in the setting of a single classical verifier and two quantum provers, and exhibit the PoK property for a non-local game for the local Hamiltonian problem. More specifically, we construct an extractor which, given oracle access to a provers’ strategy that leads to high acceptance probability, is able to reconstruct the ground state of a local Hamiltonian. Our result can be seen as a new form of self-testing, where, in addition to certifying a pre-shared entangled state and the prover’s strategy, the verifier also certifies a local quantum state. This technique thus provides a method to ascertain that a prover has access to a quantum system, in particular, a ground state, thus indicating a new level of verification for a proof of quantumness.

Characterising memory in quantum channel discrimination via constrained separability problems

Mon, 17 Mar 2025 00:00:00 +0000

Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.

Experimental quantum randomness enhanced by a quantum network

Mon, 17 Mar 2025 00:00:00 +0000

The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be unpredictable. However, it is also highly susceptible to noise. Here, we show that extending the conventional bipartite Bell scenario to hybrid quantum networks – which incorporate both quantum channels and entanglement sources – enhances the robustness of certifiable randomness. Our protocol even enables randomness to be certified from Bell-local states, broadening the range of quantum states useful for this task. Through both theoretical analysis and experimental validation in a photonic network, we demonstrate enhanced performance and improved noise resilience.

Higher-Order Quantum Operations

Mon, 17 Mar 2025 00:00:00 +0000

An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum operations$\unicode{x2014}$are fundamental to modern quantum theory, extending beyond basic state preparations, evolutions, and measurements described by the Born rule. These operations naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. This Review Article provides both a pedagogical introduction to the framework of higher-order quantum operations and a comprehensive survey of current literature, illustrated through physical examples. We conclude by identifying open problems and future research directions in this rapidly evolving field.

An operating system for executing applications on quantum network nodes

Wed, 12 Mar 2025 00:00:00 +0000

An operating system for executing applications on quantum network nodes

Wed, 12 Mar 2025 00:00:00 +0000

The goal of future quantum networks is to enable new internet applications that are impossible to achieve using only classical communication1,2,3. Up to now, demonstrations of quantum network applications4,5,6 and functionalities7,8,9,10,11,12 on quantum processors have been performed in ad hoc software that was specific to the experimental setup, programmed to perform one single task (the application experiment) directly into low-level control devices using expertise in experimental physics. Here we report on the design and implementation of an architecture capable of executing quantum network applications on quantum processors in platform-independent high-level software. We demonstrate the capability of the architecture to execute applications in high-level software by implementing it as a quantum network operating system—QNodeOS—and executing test programs, including a delegated computation from a client to a server13 on two quantum network nodes based on nitrogen-vacancy (NV) centres in diamond14,15. We show how our architecture allows us to maximize the use of quantum network hardware by multitasking different applications. Our architecture can be used to execute programs on any quantum processor platform corresponding to our system model, which we illustrate by demonstrating an extra driver for QNodeOS for a trapped-ion quantum network node based on a single 40Ca+ atom16. Our architecture lays the groundwork for computer science research in quantum network programming and paves the way for the development of software that can bring quantum network technology to society.

Certifying measurement incompatibility in prepare-and-measure and Bell scenarios

Mon, 03 Mar 2025 00:00:00 +0000

We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage in PM scenarios. Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario if and only if their incompatibility can be certified in a bipartite Bell scenario where the parties share a maximally entangled state. Our framework naturally suggests a hierarchy of increasingly stronger notions of incompatibility, in which more power is given to the classical simulation by increasing its dimensionality. For qubits, we give an example of measurements whose incompatibility can be certified against trit simulations, which we show is the strongest possible notion for qubits in this framework.

Integrated InP-based transmitter for continuous-variable quantum key distribution

Mon, 24 Feb 2025 00:00:00 +0000

Developing quantum key distribution (QKD) systems using monolithic photonic integrated circuits (PICs) can accelerate their adoption by a wide range of markets, thanks to the potential reduction in size, complexity of the overall system, power consumption, and production cost. In this work, we design, fabricate and characterize an InP-based PIC transmitter for continuous-variable (CV) QKD applications. In a proof-of-principle experiment implementing a pulsed Gaussian-modulated coherent state (GMCS) CV-QKD protocol over an optical fiber channel of 11 km, the system showed a performance compatible with a secret key rate of 78 kbps in the asymptotic regime. These results show the potential of InP technologies to integrate CV-QKD systems onto a monolithic platform.

Distributed Non-Interactive Zero-Knowledge Proofs

Wed, 12 Feb 2025 00:00:00 +0000

Distributed certification is a set of mechanisms that allows an all-knowing prover to convince the units of a communication network that the network’s state has some desired property, such as being 3-colorable or triangle-free. Classical mechanisms, such as proof labeling schemes (PLS), consist of a message from the prover to each unit, followed by one round of communication between each unit and its neighbors. Later works consider extensions, called distributed interactive proofs, where the prover and the units can have multiple rounds of communication before the communication among the units. Recently, Bick, Kol, and Oshman (SODA ‘22) defined a zero-knowledge version of distributed interactive proofs, where the prover convinces the units of the network’s state without revealing any other information about the network’s state or structure. In their work, they propose different variants of this model and show that many graph properties of interest can be certified with them. In this work, we define and study distributed non-interactive zero-knowledge proofs (dNIZK); these can be seen as a non-interactive version of the aforementioned model, and also as a zero-knowledge version of PLS. We prove the following: - There exists a dNIZK protocol for 3-coloring with O(log n)-bit messages from the prover and O(log n)-size messages among neighbors. - There exists a family of dNIZK protocols for triangle-freeness, that presents a trade-off between the size of the messages from the prover and the size of the messages among neighbors. - There exists a dNIZK protocol for any graph property in NP in the random oracle models, which is secure against an arbitrary number of malicious parties.

Quantum function secret sharing

Mon, 03 Feb 2025 00:00:00 +0000

We propose a quantum function secret sharing scheme in which the communication is exclusively classical. In this primitive, a classical dealer distributes a secret quantum circuit $C$ by providing shares to $p$ quantum parties. The parties on an input state $|\psi\rangle$ and a projection $\Pi$, compute values $y_i$ that they then classically communicate back to the dealer, who can then compute $\lVert \Pi C|\psi\rangle\rVert^2$ using only classical resources. Moreover, the shares do not leak much information about the secret circuit $C$. Our protocol for quantum secret sharing uses the {\em Cayley path}, a tool that has been extensively used to support quantum primacy claims. More concretely, the shares of $C$ correspond to randomized version of $C$ which are delegated to the quantum parties, and the reconstruction can be done by extrapolation. Our scheme has two limitations, which we prove to be inherent to our techniques: First, our scheme is only secure against single adversaries, and we show that if two parties collude, then they can break its security. Second, the evaluation done by the parties requires exponential time in the number of gates.

Noisy certification of continuous variables graph states

Sat, 01 Feb 2025 00:00:00 +0000

Continuous variables (CV) offer a promising platform for the development of various applications, such as quantum communication, computing, and sensing, and CV graph states represent a family of powerful entangled resource states for all these areas. In many of these protocols, a crucial aspect is the certification of the quantum state subsequently used. While numerous protocols exist, most rely on assumptions unrealistic for physical continuous variable states, such as infinite precision in quadrature measurement or the use of states requiring infinite squeezing. In this work, we adapt existing protocols to deal with these unavoidable considerations, and use them to certify their application for different quantum information tasks. More specifically, we show how CV graph states can be efficiently verified and certified even in a noisy and imperfect setting. We then discuss how our findings impact the usability of states obtained after the protocol for different applications, including quantum teleportation, computing, and sensing.

Energetic Analysis of Emerging Quantum Communication Protocols

Mon, 06 Jan 2025 00:00:00 +0000

Anonymous and private parameter estimation in networks of quantum sensors

Wed, 01 Jan 2025 00:00:00 +0000

Anonymity and privacy are two key properties of modern communication networks. In quantum networks, distributed quantum sensing has emerged as a powerful use case, with applications to clock synchronisation, detecting gravitational effects and more. In this work, we develop a new protocol that, for the first time, combines the different cryptographic properties of anonymity and privacy for the task of distributed parameter estimation. That is, we present a protocol that allows a selected subset of network participants to anonymously collaborate in estimating the average of their private parameters. Crucially, this is achieved without disclosing either the individual parameter values or the identities of the participants, neither to each other nor to the broader network.

Can outcome communication explain Bell nonlocality?

Wed, 01 Jan 2025 00:00:00 +0000

A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.

Communications sécurisées avec des variables quantiques continues

Wed, 01 Jan 2025 00:00:00 +0000

La distribution quantique de clés est une application majeure des technologies quantiques permettant la sécurisation des communications pour des données de haute confidentialité. Son déploiement pratique dans des infrastructures de réseaux nécessite des systèmes de haute performance, compacts et robustes. Dans cet article, sont présentés les concepts de base, les performances et les défis actuels de tels systèmes basés sur le codage de l’information dans des propriétés des quadratures du champ électromagnétique.

Experimentally Certified Transmission of a Quantum Message through an Untrusted and Lossy Quantum Channel via Bell's Theorem

Wed, 01 Jan 2025 00:00:00 +0000

Quantum transmission links are central elements in essentially all protocols involving the exchange of quantum messages. Emerging progress in quantum technologies involving such links needs to be accompanied by appropriate certification tools. In adversarial scenarios, a certification method can be vulnerable to attacks if too much trust is placed on the underlying system. Here, we propose a protocol in a device-independent framework, which allows for the certification of practical quantum transmission links in scenarios in which minimal assumptions are made about the functioning of the certification setup. In particular, we take unavoidable transmission losses into account by modeling the link as a completely positive trace-decreasing map. We also, crucially, remove the assumption of independent identically distributed samples, which is known to be incompatible with adversarial settings. Particular emphasis is put on a one-sided device-independent scenario, in which the sender possesses trusted resources. Finally, in view of the use of the certified transmitted states for follow-up applications, our protocol moves beyond certification of the channel to allow us to estimate the quality of the transmitted quantum message itself. To illustrate the practical relevance and the feasibility of our protocol with currently available technology, we provide an experimental implementation in the one-sided device-independent setting, based on a state-of-the-art polarization-entangled photon-pair source in a Sagnac configuration, and analyze its robustness for realistic losses and errors.

Measurement incompatibility and quantum steering via linear programming

Wed, 01 Jan 2025 00:00:00 +0000

The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP). However, the number of variables and constraints in such a formulation grows exponentially with the number of measurements, rendering it intractable for large measurement sets. In this work, we circumvent this problem by transforming the SDP into a hierarchy of linear programs that compute upper and lower bounds on the incompatibility robustness with a complexity that grows polynomially in the number of measurements. The hierarchy is guaranteed to converge and it can be applied to arbitrary measurements – including non-projective POVMs – in arbitrary dimensions. While convergence becomes impractical in high dimensions, in the case of qubits our method reliably provides accurate upper and lower bounds for the incompatibility robustness of sets with several hundred measurements in a short time using a standard laptop. We also apply our methods to qutrits, obtaining non-trivial upper and lower bounds in scenarios that are otherwise intractable using the standard SDP approach. Finally, we show how our methods can be used to construct local hidden state models for states, or conversely, to certify that a given state exhibits steering; for two-qubit quantum states, our approach is comparable to, and in some cases outperforms, the current best methods.

Privacy in networks of quantum sensors

Wed, 01 Jan 2025 00:00:00 +0000

We treat privacy in a network of quantum sensors where accessible information is limited to specific functions of the network parameters, and all other information remains private. We develop an analysis of privacy in terms of a manipulation of the quantum Fisher information matrix, and find the optimal state achieving maximum privacy in the estimation of linear combination of the unknown parameters in a network of quantum sensors. We also discuss the effect of uncorrelated noise on the privacy of the network. Moreover, we illustrate our results with an example where the goal is to estimate the average value of the unknown parameters in the network. In this example, we also introduce the notion of quasi-privacy ($\epsilon$-privacy), quantifying how close the state is to being private.

Section 06 Sciences de l’information : fondements de l’informatique, calculs, algorithmes, représentations, exploitations

Wed, 01 Jan 2025 00:00:00 +0000

La section 6 du Comité national de la recherche scientifique est, avec la section 7, une des deux sections traitant de la science informatique, et plus précisément de l’algorithmique et de la combinatoire, du calcul, du logiciel, de la sécurité, des réseaux et systèmes distribuées, des données et connaissances, de l’intelligence artificielle et de l’aide à la décision, ainsi que de la bio-informatique et de l’informatique quantique. Ce rapport présente le périmètre thématique de la section, discute de la place des femmes ainsi que des évolutions récentes des pratiques de recherche, présente la conjoncture des différents thèmes de recherche et enfin décrit les carrières au CNRS des chercheurs et chercheuses de la section.

Subspace preserving quantum convolutional neural network architectures

Wed, 01 Jan 2025 00:00:00 +0000

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.

Experimental demonstration of Continuous-Variable Quantum Key Distribution with a silicon photonics integrated receiver

Wed, 25 Dec 2024 00:00:00 +0000

Quantum Key Distribution (QKD) is a prominent application in the field of quantum cryptography providing information-theoretic security for secret key exchange. The implementation of QKD systems on photonic integrated circuits (PICs) can reduce the size and cost of such systems and facilitate their deployment in practical infrastructures. To this end, continuous-variable (CV) QKD systems are particularly well-suited as they do not require single-photon detectors, whose integration is presently challenging. Here we present a CV-QKD receiver based on a silicon PIC capable of performing balanced detection. We characterize its performance in a laboratory QKD setup using a frequency multiplexed pilot scheme with specifically designed data processing allowing for high modulation and secret key rates. The obtained excess noise values are compatible with asymptotic secret key rates of 2.4 Mbit/s and 220 kbit/s at an emulated distance of 10 km and 23 km, respectively. These results demonstrate the potential of this technology towards fully integrated devices suitable for high-speed, metropolitan-distance secure communication.

Nonlocality and self-testing graph states with bounded communication

Thu, 19 Dec 2024 00:00:00 +0000

Graph states correspond to mathematical graphs and exhibit nonlocality, as no local hidden-variable (lhv) model can predict all their measurement correlations. In this thesis, we study extensions of nonlocality in graph states, where we allow lhv models to engage in a round of distance-ddc classical communication along the graph’s edges, denote as r-lhv* models. Barrett et al.[2007] were the first to report correlations from local Pauli measurements on a particular family of graphs states to refute an r-lhv* description. Their result was pivotal in demonstrating a separation between classical and quantum computing regarding circuit depth without relying on any complexity-theoretic assumptions. Inspired by Barrett et al.’s findings, our first result is a systematic extension of any graph state to what we call `inflated graph state’. These states exhibit correlations that refute any communication-assisted lhv model. For certain graph topologies, the size and number of measurements can be optimized. The smallest graph exhibiting nonlocal correlations from Pauli measurements, while permitting nearest-neighbor communication, is the circle of five qubits. Additionally, the linear graph of four vertices presents the smallest possible such violation using binary inputs and outputs. Our second result explores the application of the setting compatible with r-lhv* models to self-testing, a method to infer the state and operations based purely on the statistics of measurement outcomes. In particular, all graph states can be self-tested in the standard setting, where parties are not allowed to communicate. We develop a self-testing method within the framework of bounded classical communication, demonstrating that certain graph states can still be robustly self-tested even when communication is allowed. Specifically, we provide an explicit self-test for the circular graph state, as well as the honeycomb and square cluster states — both of which are known to be universal resources for measurement-based quantum computation. Given that communication typically obstructs the self-testing of graph states, we also present a procedure to robustly self-test any graph state by using the inflated graph states, which exhibit nonlocal correlations against bounded classical communication. We expect these findings to have be useful in an interactive prover scheme while relaxing the standard assumption that the provers cannot communicate, the provers might now engage in distance-bounded classical communication. While the above results are only valid for qubits –two-dimensional systems–, we show that correlations the defy r-lhv* models also exists for graph states in so-called qudit systems for any finite, odd, prime dimension d. For this purpose, we study nonlocality in qudit systems in the standard Bell scenario without communication, as part of our third result. First, we construct specific correlations that defy lhv models deterministically, as well as correlations that do so with a constant number of measurements, relying on operators innate to higher-dimensional systems than the qudit at hand. Then, we propose a family of Bell inequalities using correlations related to a given entangled state’s Wigner negativity. For a violation with stabilizer states, we resort to Pauli measurements under the adjoint action of a generalization of the qubit pi/8 gate, an abstraction of the Clauser-Horne-Shimony-Holt inequality. This result can be extended to multipartite stabilizer states, including graph states, where we demonstrate violations robust against bounded classical communication.

System Integration of High-Performance Continuous-Variable Quantum Key Distribution

Mon, 09 Dec 2024 00:00:00 +0000

Quantum Key Distribution (QKD) is the most prominent and the most mature application of quantum communications. It provides a way for two trusted users, usually named Alice and Bob, once they are provided with a public quantum channel and a public but authenticated classical channel, to exchange a secret key with a security based, not on computational assumptions as it is currently the case with classical cryptography, but on the laws of Physics, and hence, protects even against unbounded adversaries. Combined with a perfectly secure encryption scheme, QKD allows for secure message transmission with information-theoretic security. QKD protocols rely on the no-cloning theorem, and the basic principle that measuring a quantum system inherently modifies its state. These protocols can be mostly divided in two families: Discrete Variable (DV) protocols where the information is encoded on discrete properties of single photons, and Continuous Variable (CV) protocols where the information is encoded on continuous degrees of freedom; and in practice the quadratures of the electromagnetic field. While DV protocols have more maturity, can achieve longer distances, and require less signal processing, their CV counterparts can work at room temperature with high efficiency and at high rate. This thesis mainly focuses on CV-QKD protocols, and tackles several challenges associated with the integration of CV-QKD systems. It showcases the integration of optical components to create a silicon photonics-based receiver for CV-QKD, and benchmark its performance in a full CV-QKD setup, showing an operation up to 23 km of distance. It also showcases the software integration of our CV-QKD experimental platform, as an open-source suite called QOSST: Quantum Open Software for Secure Transmissions. The software performs hardware control, digital signal processing for Alice and Bob (including clock, frequency and phase synchronisation), classical communications with authentication, parameter estimation and secret key rate computation for CV-QKD operations. It is hardware-agnostic and can run in a number of scenarios. It also provides extensive documentation, in the hope that it can help reduce the barrier to enter the world of CV-QKD research, as well as that it can be expanded and improved by other interested groups. The autonomy of the software allows the finding of crucial relationships between signal processing parameters and performance. Using our setup, we demonstrate positive key rates up to 25 km of fiber distance. Our prototype is then integrated into a deployed network in the Paris area, in particular, showing the feasibility on a 15 km deployed link between two remote nodes in Paris. This quantum communication infrastructure is also used to deploy DV-QKD commercial systems, and perform an experiment with a trusted node efficiently secured with Post-Quantum Cryptography on a 57 km link. The energetic cost of CV-QKD is also investigated, both with a hardware-dependent approach and a more theoretical approach to give lower bounds on the energetic consumption. While the theoretical approach gives the global scaling, the hardware dependent approach shows what to expect for the first generation of CV-QKD systems, as well as an interesting comparison between the hardware cost and the post-processing cost. Finally, the detectors used for the CV-QKD setup are considered for another protocol involving the verification of Boson Sampling. Initial simulations and experimental preparation highlight the challenges involved in such an experiment.

Photonic quantum generative adversarial networks for classical data

Sun, 01 Dec 2024 00:00:00 +0000

In generative learning, models are trained to produce new samples that follow the distribution of the target data. These models were historically difficult to train, until proposals such as generative adversarial networks (GANs) emerged, where a generative and a discriminative model compete against each other in a minimax game. Quantum versions of the algorithm have since been designed for the generation of both classical and quantum data. While most work so far has focused on qubit-based architectures, in this article we present a quantum GAN based on linear optical circuits and Fock-space encoding, which makes it compatible with near-term photonic quantum computing. We demonstrate that the model can learn to generate images by training the model end-to-end experimentally on a single-photon quantum processor.

Increasing the secret key rate of satellite-to-ground entanglement-based QKD assisted by adaptive optics

Tue, 26 Nov 2024 00:00:00 +0000

Future quantum networks will be composed of both terrestrial links for metropolitan and continent-scale connections and space-based links for global coverage and infrastructure resilience. However, the propagation of quantum signals through the atmosphere is severely impacted by the effects of turbulence. This is even more the case for entanglement-based quantum communication protocols requiring two free-space channels to be considered simultaneously. In this work, we assess the advantage of turbulence mitigation by adaptive optics, in particular during daytime link operation, so as to increase the coupling of the received signal into an optical fiber. We show in particular that this improves the performance of entanglement-based quantum key distribution by up to a few hundred bits per second when compared with the uncorrected scenario

Experimental Sample-Efficient and Device-Independent GHZ State Certification

Mon, 25 Nov 2024 00:00:00 +0000

The certification of quantum resources is a critical tool in the development of quantum information processing. In particular, quantum state verification is a fundamental building block for communication and computation applications, determining whether the involved parties can trust the resources at hand or whether the application should be aborted. Self-testing methods have been used to tackle such verification tasks in a device-independent (DI) setting. However, these approaches commonly consider the limit of large (asymptotic), identically and independently distributed (IID) samples, which weakens the DI claim and poses serious challenges to their experimental implementation. Here we overcome these challenges by adopting a theoretical protocol enabling the certification of quantum states in the few-copies and non-IID regime and by leveraging a high-fidelity multipartite entangled photon source. This allows us to show the efficient and device-independent certification of a single copy of a four-qubit GHZ state that can readily be used for the robust and reliable implementation of quantum information tasks.

Realizing a Compact, High-Fidelity, Telecom-Wavelength Source of Multipartite Entangled Photons

Mon, 25 Nov 2024 00:00:00 +0000

Multipartite entangled states are an essential building block for advanced quantum networking applications. Realizing such tasks in practice puts stringent requirements on the characteristics of the states in terms of fidelity and generation rate, along with a desired compatibility with telecommunication network deployment. Here, we demonstrate a photonic platform design capable of producing high-fidelity Greenberger-Horne-Zeilinger (GHZ) states, at telecom wavelength and in a compact and scalable configuration. Our source relies on spontaneous parametric down-conversion in a layered Sagnac interferometer, which only requires a single nonlinear crystal. This enables the generation of highly indistinguishable photon pairs, leading by entanglement fusion to four-qubit polarization-entangled GHZ states with fidelity up to $(94.73 \pm 0.21)%$ with respect to the ideal state, at a rate of 1.7Hz. We provide a complete characterization of our source and highlight its suitability for practical quantum network applications.

A unifying framework for differentially private quantum algorithms