Uta Isabella Meyer | 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.

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.

Nonlocality & Self-testing Graph States with Bounded Communication

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

Félicitations Dr.Meyer !

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.

Bell Nonlocality from Wigner Negativity in Qudit Systems

Wed, 12 Jun 2024 00:00:00 +0000

Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits. For higher-dimensional systems, certain results for their two-level counterpart, like Bell violations with stabilizer states and Clifford operators, do not generalize. On the other hand, similar to continuous variable systems, Wigner negativity is necessary for nonlocality in qudit systems. We propose a family of Bell inequalities that inquire correlations related to the Wigner negativity of stabilizer states under the adjoint action of a generalization of the qubit $\pi/8$ gate, which, in the bipartite case, is an abstraction of the CHSH inequality. The classical bound is simple to compute, and a specified stabilizer state maximally violates the inequality among all qudit states based on the Wigner negativity and an inequality between the 1-norm and the maximum norm. The Bell operator not only serves as a measure for the singlet fraction but also quantifies the volume of Wigner negativity. Furthermore, we give deterministic Bell violations, as well as violations with a constant number of measurements, for the Bell state relying on operators innate to higher-dimensional systems than the qudit at hand.

Self-Testing Graph States Permitting Bounded Classical Communication

Sun, 05 May 2024 00:00:00 +0000

Self-testing identifies quantum states and correlations that exhibit non-locality, distinguishing them, up to local transformations, from other quantum states. Due to their strong non-locality, all graph states can be self-tested with strictly local measurement devices. Moreover, graph states display non-local correlations even when bounded classical communication on the underlying graph is permitted, a feature that has found applications in proving a circuit-depth separation between classical and quantum computing. In the framework of bounded classical communication, we show that certain graph states with appropriate symmetry can be robustly self-tested, by providing an explicit self-test for the circular graph state and the honeycomb cluster state. Since communication generally obstructs self-testing of graph states, we further provide a procedure to robustly self-test any graph state from larger ones that exhibit non-local correlations in the communication scenario. Furthermore, in the standard setup without classical communication, we demonstrate that any graph state from an underlying connected graph with at least three vertices can be robustly self-tested using only Pauli measurements.

Inflated Graph States Refuting Communication-Assisted LHV Models

Wed, 05 Jul 2023 00:00:00 +0000

Standard Bell inequalities hold when distant parties are not allowed to communicate. Barrett et al. found correlations from Pauli measurements on certain network graphs refute a local hidden variable (LHV) description even allowing some communication along the graph. This has recently found applications in proving separation between classical and quantum computing, in terms of shallow circuits, and distributed computing. The correlations presented by Barrett et al. can be understood as coming from an extension of three party GHZ state correlations which can be embedded on a graph state. In this work, we propose systematic extensions of any graph state, which we dub inflated graph states such that they exhibit correlations which refute any communication assisted LHV model. We further show the smallest possible such example, with a 7-qubit linear graph state, as well as specially crafted smaller examples with 5 and 4 qubits. The latter is the smallest possible violation using binary inputs and outputs.