Ulysse Chabaud | LIP6 - Équipe QI

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.

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.

Ulysse Chabaud - Not specified

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

Not specified

Ce séminaire, donné par Ulysse Chabaud, aura lieu le 12 February 2025, à 15:0. Il aura lieu en salle Not specified.

Vous trouverez un plan du campus ici.

Résumé

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On the role of coherence for quantum computational advantage

Sun, 24 Nov 2024 00:00:00 +0000

Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, magic and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical simulation, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers.

Towards quantum advantage with photonic state injection

Sun, 24 Nov 2024 00:00:00 +0000

We propose a new scheme for near-term photonic quantum device that allows 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 not believed to be tackled classically. We explain how circuits made of linear optical architectures separated by state injections are keen for experimental implementation. In addition, we give theoretical results on 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 subroutines of learning algorithms named probability estimation, and we show the state injection scheme we propose may offer a potential quantum advantage in a regime that can be more easily achieved that state-of-the-art adaptive techniques. Our analysis offers new possibilities for near-term advantage that require to tackle fewer experimental difficulties.

Towards an Experimental Implementation of Efficient Verification of Boson Sampling

Sun, 23 Jun 2024 00:00:00 +0000

Experimental cheat-sensitive quantum weak coin flipping

Fri, 01 Dec 2023 00:00:00 +0000

As in modern communication networks, the security of quantum networks will rely on complex cryptographic tasks that are based on a handful of fundamental primitives. Weak coin flipping (WCF) is a significant such primitive which allows two mistrustful parties to agree on a random bit while they favor opposite outcomes. Remarkably, perfect information-theoretic security can be achieved in principle for quantum WCF. Here, we overcome conceptual and practical issues that have prevented the experimental demonstration of this primitive to date, and demonstrate how quantum resources can provide cheat sensitivity, whereby each party can detect a cheating opponent, and an honest party is never sanctioned. Such a property is not known to be classically achievable with information-theoretic security. Our experiment implements a refined, loss-tolerant version of a recently proposed theoretical protocol and exploits heralded single photons generated by spontaneous parametric down conversion, a carefully optimized linear optical interferometer including beam splitters with variable reflectivities and a fast optical switch for the verification step. High values of our protocol benchmarks are maintained for attenuation corresponding to several kilometers of telecom optical fiber.

Experimental cheat-sensitive quantum weak coin flipping

Fri, 01 Dec 2023 00:00:00 +0000

Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

Fri, 02 Dec 2022 00:00:00 +0000

Quantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting - a promising paradigm for the realisation of universal, scalable, and fault-tolerant quantum computing - contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way towards practical demonstrations of continuous-variable contextuality, and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

Fri, 02 Dec 2022 00:00:00 +0000

Experimental cheat-sensitive quantum weak coin flipping

Thu, 17 Nov 2022 00:00:00 +0000

Efficient verification of Boson Sampling

Mon, 15 Nov 2021 00:00:00 +0000

The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. To that end, we derive an efficient protocol for verifying with single-mode Gaussian measurements the output states of a large class of continuous variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, with and without i.i.d. assumption, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous variable multi-mode quantum states.

Efficient verification of Boson Sampling

Mon, 15 Nov 2021 00:00:00 +0000

Optimal quantum-programmable projective measurements with coherent states

Fri, 01 Oct 2021 00:00:00 +0000

We consider a device which can be programed using coherent states of light to approximate a given projective measurement on an input coherent state. We provide and discuss three practical implementations of this programmable projective measurement device with linear optics, involving only balanced beam splitters and single photon threshold detectors. The three schemes optimally approximate any projective measurement onto a program coherent state. We further extend these to the case where there are no assumptions on the input state. In this setting, we show that our scheme enables an efficient verification of an unbounded untrusted source with only local coherent states, balanced beam splitters, and threshold detectors. Exploiting the link between programmable measurements and generalized swap test, we show as a direct application that our schemes provide an asymptotically quadratic improvement in existing quantum fingerprinting protocol to approximate the Euclidean distance between two unit vectors.

Classical simulation of Gaussian quantum circuits with non-Gaussian input states

Tue, 06 Jul 2021 00:00:00 +0000

We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of continuous-variable quantum states to the multimode setting and relate the stellar rank of the input non-Gaussian states, a recently introduced measure of non- Gaussianity, to the cost of evaluating classically the output probability densities of these circuits. Our results have consequences for the strong simulability of a large class of near-term continuous-variable quantum circuits.

Quantum machine learning with adaptive linear optics

Mon, 05 Jul 2021 00:00:00 +0000

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements. We then challenge these quantum algorithms by deriving classical simulation algorithms for the tasks of output probability estimation and overlap estimation. We obtain different classical simulability regimes for these two computational tasks in terms of the number of adaptive measurements and input photons. In both cases, our results set explicit limits to the range of parameters for which a quantum advantage can be envisaged with adaptive linear optics compared to classical machine learning algorithms: we show that the number of input photons and the number of adaptive measurements cannot be simultaneously small compared to the number of modes. Interestingly, our analysis leaves open the possibility of a near-term quantum advantage with a single adaptive measurement.

Quantum machine learning with adaptive linear optics

Mon, 05 Jul 2021 00:00:00 +0000

Witnessing Wigner Negativity

Tue, 08 Jun 2021 00:00:00 +0000

Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum technologies emerge, the need to identify and characterize the resources which provide an advantage over existing classical technologies becomes more pressing. Here we derive witnesses for Wigner negativity of quantum states, based on fidelities with Fock states, which can be reliably measured using standard detection setups. They possess a threshold expected value indicating whether the measured state exhibits the desired property or not. We phrase the problem of finding the threshold values for our witnesses as an infinite-dimensional linear optimisation. By relaxing and restricting the corresponding linear programs, we derive two hierarchies of semidefinite programs, which provide numerical sequences of increasingly tighter upper and lower bounds for the threshold values. We further show that both sequences converge to the threshold value. Moreover, our witnesses form a complete family - each Wigner negative state is detected by at least one witness - thus providing a reliable method for experimentally witnessing Wigner negativity of quantum states from few measurements. From a foundational perspective, our work provides insights on the set of positive Wigner functions which still lacks a proper characterisation.

Witnessing Wigner Negativity

Tue, 08 Jun 2021 00:00:00 +0000

Certification of Non-Gaussian States with Operational Measurements

Thu, 03 Jun 2021 00:00:00 +0000

We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous-variable quantum states, and show that certification of high-order non-Gaussian features can be carried out experimentally with current technology.

Quantum weak coin flipping with a single photon

Wed, 19 Aug 2020 00:00:00 +0000

Weak coin flipping is among the fundamental cryptographic primitives which ensure the security of modern communication networks. It allows two mistrustful parties to remotely agree on a random bit when they favor opposite outcomes. Unlike other two-party computations, one can achieve information-theoretic security using quantum mechanics only: both parties are prevented from biasing the flip with probability higher than $1/2+\epsilon$, where $\epsilon$ is arbitrarily low. Classically, the dishonest party can always cheat with probability $1$ unless computational assumptions are used. Despite its importance, no physical implementation has been proposed for quantum weak coin flipping. Here, we present a practical protocol that requires a single photon and linear optics only. We show that it is fair and balanced even when threshold single-photon detectors are used, and reaches a bias as low as $\epsilon=1/\sqrt{2}-1/2\approx 0.207$. We further show that the protocol may display quantum advantage over a few hundred meters with state-of-the-art technology.

Breaking simple quantum position verification protocols with little entanglement

Mon, 17 Aug 2020 00:00:00 +0000

Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $\theta$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (e.g. $\pi/6$), and show no $\theta$ allows to tolerate errors higher than $\simeq 5\cdot 10^{-3}$ against adversaries holding two ebits per protocol’s qubit.

Continuous variable quantum advantages and applications in quantum optics

Wed, 22 Jul 2020 00:00:00 +0000

Quantum physics has led to a revolution in our conception of the nature of our world and is now bringing about a technological revolution. The use of quantum information promises indeed applications that outperform those of today’s so-called classical devices. Continuous variable quantum information theory refers to the study of quantum information encoded in continuous degrees of freedom of quantum systems. This theory extends the mathematical study of quantum information to quantum states in Hilbert spaces of infinite dimension. It offers different perspectives compared to discrete variable quantum information theory and is particularly suitable for the description of quantum states of light. Quantum optics is thus a natural experimental platform for developing quantum applications in continuous variable. This thesis focuses on three main questions: where does a quantum advantage, that is, the ability of quantum machines to outperform classical machines, come from? How to ensure the proper functioning of a quantum machine? What advantages can be gained in practice from the use of quantum information? These three questions are at the heart of the development of future quantum technologies and we provide several answers within the frameworks of continuous variable quantum information and linear quantum optics.

Continuous Variable Quantum Advantages and Applications in Quantum Optics

Wed, 01 Jul 2020 00:00:00 +0000

Abstract :
Quantum physics has led to a revolution in our conception of the nature of our world and is now bringing about a technological revolution. The use of quantum information promises indeed applications that outperform those of today’s so-called classical devices. Continuous variable quantum information theory refers to the study of quantum information encoded in continuous degrees of freedom of quantum systems. This theory extends the mathematical study of quantum information to quantum states in Hilbert spaces of infinite dimension. It offers different perspectives compared to discrete variable quantum information theory and is particularly suitable for the description of quantum states of light. Quantum optics is thus a natural experimental platform for developing quantum applications in continuous variable. This thesis focuses on three main questions: where does a quantum advantage, that is, the ability of quantum machines to outperform classical machines, come from? How to ensure the proper functioning of a quantum machine? What advantages can be gained in practice from the use of quantum information? These three questions are at the heart of the development of future quantum technologies and we provide several answers within the frameworks of continuous variable quantum information and linear quantum optics. Quantum advantage in continuous variable comes in particular from the use of so-called non-Gaussian quantum states. We introduce the stellar formalism to characterize these states. We then study the transition from classically simulable models to models universal for quantum computing. We show that quantum computational supremacy, the dramatic speedup of quantum computers over their classical counterparts, may be realised with non-Gaussian states and Gaussian measurements. Quantum certification denotes the methods seeking to verify the correct functioning of a quantum machine. We consider certification of quantum states in continuous variable, introducing several protocols according to the assumptions made on the tested state. We develop efficient methods for the verification of a large class of multimode quantum states, including the output states of the Boson Sampling model, enabling the experimental verification of quantum supremacy with photonic quantum computing. We give several new examples of practical applications of quantum information in linear quantum optics. Generalising the swap test, we highlight a connection between the ability to distinguish two quantum states and the ability to perform universal programmable quantum measurements, for which we give various implementations in linear optics, based on the use of single photons or coherent states. Finally, we obtain, thanks to linear optics, the first implementation of a quantum protocol for weak coin flipping, a building block for many cryptographic applications.

Quantum certification and benchmarking

Wed, 17 Jun 2020 00:00:00 +0000

Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can be reached and their functioning guaranteed. This Expert Recommendation provides a brief overview of the known characterization methods of certification, benchmarking, and tomographic recovery of quantum states and processes, as well as their applications in quantum computing, simulation, and communication.

Quantum certification and benchmarking

Wed, 17 Jun 2020 00:00:00 +0000

Building trust for continuous variable quantum states

Mon, 01 Jun 2020 00:00:00 +0000

We first introduce heterodyne quantum state tomography, a reliable method for continuous variable quantum state certification which directly yields the elements of the density matrix of the state considered and analytical confidence intervals, using heterodyne detection. This method neither needs mathematical reconstruction of the data, nor discrete binning of the sample space, and uses a single Gaussian measurement setting. Beyond quantum state tomography and without its identical copies assumption, we also derive a general protocol for verifying continuous variable pure quantum states with Gaussian measurements against fully malicious adversaries. In particular, we make use of a De Finetti reduction for infinite-dimensional systems. As an application, we consider verified universal continuous variable quantum computing, with a computational power restricted to Gaussian operations and an untrusted non-Gaussian states source. These results are obtained using a new analytical estimator for the expected value of any operator acting on a continuous variable quantum state with bounded support over Fock basis, computed with samples from heterodyne detection of the state.

Stellar representation of non-Gaussian quantum states

Fri, 14 Feb 2020 00:00:00 +0000

The so-called stellar formalism allows to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q-function in phase-space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q-function, the stellar hierarchy. We give an operational characterisation of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering, and continuous variable quantum computing.

Stellar representation of non-Gaussian quantum states

Fri, 14 Feb 2020 00:00:00 +0000

On the permanent of Sylvester-Hadamard matrices

Tue, 15 Oct 2019 00:00:00 +0000

We prove a conjecture due to Wanless about the permanent of Hadamard matrices in the particular case of Sylvester-Hadamard matrices. Namely we show that for all n greater or equal to 2, the dyadic valuation of the permanent of the Sylvester-Hadamard matrix of order n is equal to the dyadic valuation of n!. As a consequence, the permanent of the Sylvester-Hadamard matrix of order n doesn’t vanish for n greater or equal to 2.

Optimal quantum-programmable projective measurement with linear optics

Fri, 14 Dec 2018 00:00:00 +0000

We present a scheme for a universal device which can be programed by quantum states to approximate a chosen projective measurement to a given precision. Our scheme can be viewed as an extension of the swap test to the instance where one state is supplied many times. As such, it has many potential applications given the variety of quantum information tasks which make use of the swap test. In particular, we show that our scheme is optimal for state discrimination under the one-sided error requirement, and optimally approximates any projective measurement. Furthermore, we propose a practical implementation of our scheme with passive linear optics, which involves a simple interferometer composed only of balanced beam splitters.

Optimal quantum-programmable projective measurement with linear optics

Fri, 14 Dec 2018 00:00:00 +0000