Bilocal Bell Inequalities Violated by the Quantum Elegant Joint Measurement

Certifying Network Topologies and Nonlocalities of Triangle Quantum Networks

Quantum networks promise unprecedented advantages in information processing and open up intriguing new opportunities in fundamental research, where network topology and network nonlocality fundamentally underlie these applications. Hence, the detections of network topology and nonlocality are crucial, which, however, remain an open problem. Here, we conceive and experimentally demonstrate to determine the network topology and network nonlocality hosted by a triangle quantum network comprising three parties, within and beyond Bell theorem, with a general witness operator for the first time. We anticipate that this unique approach may stimulate further studies toward the efficient characterization of large complex quantum networks so as to better harness the advantage of quantum networks for quantum information applications.

Quantifying the Intrinsic Randomness of Quantum Measurements

Intrinsic quantum randomness is produced when a projective measurement on a given basis is implemented on a pure state that is not an element of the basis. The prepared state and implemented measurement are perfectly known, yet the measured result cannot be deterministically predicted. In realistic situations, however, measurements and state preparation are always noisy, which introduces a component of stochasticity in the outputs that is not a consequence of the intrinsic randomness of quantum theory. Operationally, this stochasticity is modeled through classical or quantum correlations with an eavesdropper, Eve, whose goal is to make the best guess about the outcomes produced in the experiment. In this Letter, we study Eve's maximum guessing probability when she is allowed to have correlations with both the state and the measurement. We show that, unlike the case of projective measurements (as it was already known) or pure states (as we prove), in the setting of generalized measurements and mixed states, Eve's guessing probability differs depending on whether she can prepare classically or quantumly correlated strategies.

Multipartite Nonlocality in Clifford Networks

We adopt a resource-theoretic framework to classify different types of quantum network nonlocality in terms of operational constraints placed on the network. One type of constraint limits the parties to perform local Clifford gates on pure stabilizer states, and we show that quantum network nonlocality cannot emerge in this setting. Yet, if the constraint is relaxed to allow for mixed stabilizer states, then network nonlocality can indeed be obtained. We additionally show that bipartite entanglement is sufficient for generating all forms of quantum network nonlocality when allowing for postselection, a property analogous to the universality of bipartite entanglement for generating all forms of multipartite entangled states.

Certification of non-classicality in all links of a photonic star network without assuming quantum mechanics

Networks composed of independent sources of entangled particles that connect distant users are a rapidly developing quantum technology and an increasingly promising test-bed for fundamental physics. Here we address the certification of their post-classical properties through demonstrations of full network nonlocality. Full network nonlocality goes beyond standard nonlocality in networks by falsifying any model in which at least one source is classical, even if all the other sources are limited only by the no-signaling principle. We report on the observation of full network nonlocality in a star-shaped network featuring three independent sources of photonic qubits and joint three-qubit entanglement-swapping measurements. Our results demonstrate that experimental observation of full network nonlocality beyond the bilocal scenario is possible with current technology.

Entanglement Swapping and Quantum Correlations via Symmetric Joint Measurements

We use hyperentanglement to experimentally realize deterministic entanglement swapping based on quantum elegant joint measurements. These are joint projections of two qubits onto highly symmetric, isoentangled bases. We report measurement fidelities no smaller than 97.4%. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray into entangled measurements and nonlocality beyond the paradigmatic Bell state measurement and they show the relevance of more general measurements in entanglement swapping scenarios.

Bell nonlocality in networks

Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

Nonlocality for Generic Networks

Bell's theorem shows that correlations created by a single entangled quantum state cannot be reproduced classically. Such correlations are called nonlocal. They are the elementary manifestation of a broader phenomenon called network nonlocality, where several entangled states shared in a network create network nonlocal correlations. In this Letter, we provide the first class of strategies producing nonlocal correlations in generic networks. In these strategies, called color matching (CM), any source takes a color at random or in superposition, where the colors are labels for a basis of the associated Hilbert space. A party (besides other things) checks if the color of neighboring sources match. We show that in a large class of networks without input, well-chosen quantum CM strategies result in nonlocal correlations that cannot be produced classically. For our construction, we introduce the graph theoretical concept of rigidity of classical strategies in networks, and using the Finner inequality, establish a deep connection between network nonlocality and graph theory. In particular, we establish a link between CM strategies and the graph coloring problem. This work is extended in a longer paper [35M.-O. Renou, Phys. Rev. A 105, 022408 (2022)PLRAAN2469-992610.1103/PhysRevA.105.022408], where we introduce a second family of rigid strategies called token counting, leading to network nonlocality.

Full Network Nonlocality

Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theory-independent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.

Nonlocality, Steering, and Quantum State Tomography in a Single Experiment

We investigate whether paradigmatic measurements for quantum state tomography, namely mutually unbiased bases and symmetric informationally complete measurements, can be employed to certify quantum correlations. For this purpose, we identify a simple and noise-robust correlation witness for entanglement detection, steering, and nonlocality that can be evaluated based on the outcome statistics obtained in the tomography experiment. This allows us to perform state tomography on entangled qutrits, a test of Einstein-Podolsky-Rosen steering and a Bell inequality test, all within a single experiment. We also investigate the trade-off between quantum correlations and subsets of tomographically complete measurements as well as the quantification of entanglement in the different scenarios. Finally, we perform a photonics experiment in which we demonstrate quantum correlations under these flexible assumptions, namely with both parties trusted, one party untrusted and both parties untrusted.