A two-qubit Bell inequality for which POVM measurements are relevant

Abstract

A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to projective ones. In particular, the presented Bell inequality requires POVMs in order to be maximally violated by a maximally entangled two-qubit state. This answers a question raised by N. Gisin.

7 pages, 1 figure

References in corpus (8)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• The Communication Cost of Simulating Bell Correlations
• Testing the Hilbert space dimension
• A lower bound on the dimension of a quantum system given measured data
• Noise robustness of the nonlocality of entangled quantum states
• Operator Space theory: a natural framework for Bell inequalities
• Bounds on Quantum Correlations in Bell Inequality Experiments

Cited by in corpus (41)

• Quantum Steering
• All Entangled Quantum States Are Nonlocal
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Bell nonlocality in networks
• Simulating positive-operator-valued measures with projective measurements
• Genuine hidden quantum nonlocality
• Optimal randomness certification from one entangled bit
• Self-testing non-projective quantum measurements in prepare-and-measure experiments
• Operational framework for quantum measurement simulability
• Device-Independent Certification of a Nonprojective Qubit Measurement
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Quantum measurements on finite dimensional systems: relabeling and mixing
• Most incompatible measurements for robust steering tests
• Characterizing finite-dimensional quantum behavior
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
• Entropy bounds for multiparty device-independent cryptography
• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• Classical Cost of Transmitting a Qubit
• Quantum steering with positive operator valued measures
• Joint measurability in nonequilibrium quantum thermodynamics
• Compounds of symmetric informationally complete measurements and their application in quantum key distribution
• Device-independent self-testing of unsharp measurements
• Nonlocality activation in a photonic quantum network
• High-fidelity, multi-qubit generalized measurements with dynamic circuits
• Implementation of discrete positive operator valued measures on linear optical systems using cosine-sine decomposition
• Measurement-based Multipartite Entanglement Inflation
• Simulation of positive operator-valued measures and quantum instruments via quantum state preparation algorithms
• Quantifying unsharpness of observables in an outcome-independent way
• Limits of network nonlocality probed by time-like separated observers
• Analytic quantification of the singlet nonlocality for the first Bell's inequality
• Ex ante versus ex post equilibria in classical Bayesian games with a nonlocal resource
• A higher quantum bound for the Vértesi-Bene-Bell-inequality and the role of POVMs regarding its threshold detection efficiency
• POVMs are equivalent to projections for perfect state exclusion of three pure states in three dimensions
• General measurements with limited resources and their application to quantum unambiguous state discrimination
• Bounding conditional entropy of bipartite states with Bell operators
• Nonlocality in Remote State Preparation vis-a-vis Teleportation
• Randomness-free Detection of Non-projective Measurements: Qubits & beyond
• Certifying the activation of Bell nonlocality with finite data
• New assessment on the nonlocality of correlation boxes
• Maximal device-independent randomness in every dimension
• Sequential information theoretic protocols in continuous variable systems