General method for constructing local-hidden-variable models for entangled quantum states

Abstract

Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and that can be implemented by semidefinite programming. This method can be applied to any given state and for the construction of new examples of states with local hidden-variable models for both projective and general measurements. As applications we provide a lower bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those which arise from physical noise models, Bell-diagonal states, and noisy GHZ and W states.

Published version with new title and abstract, improved presentation and new examples of LHV states. Codes are available at https://github.com/paulskrzypczyk/localhiddenstatemodels (please cite this paper if you use them). See also the related work by F. Hirsch et al arXiv:1512.00262

References in corpus (12)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• A complete family of separability criteria
• Bloch vectors for qudits
• Taming multiparticle entanglement
• Quantifying Entanglement with Witness Operators
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Grothendieck's constant and local models for noisy entangled quantum states
• Noise robustness of the nonlocality of entangled quantum states
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Local hidden--variable models for entangled quantum states
• Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality

Cited by in corpus (62)

• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
• Simulating positive-operator-valued measures with projective measurements
• Device-independent entanglement certification of all entangled states
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• Quantum measurement incompatibility does not imply Bell nonlocality
• Algorithmic construction of local hidden variable models for entangled quantum states
• Quantum states with a positive partial transpose are useful for metrology
• Measurement incompatibility does not give rise to Bell violation in general
• Semidefinite programming relaxations for quantum correlations
• Continuous variable steering and incompatibility via state-channel duality
• Entanglement without hidden nonlocality
• Most incompatible measurements for robust steering tests
• The geometry of the Einstein--Podolsky--Rosen correlations
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Measurement-device-independent entanglement and randomness estimation in quantum networks
• Super-Activation of Quantum Steering
• Maximum nonlocality in the (3,2,2) scenario
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Mapping Criteria of Nonlocality-Steerability in Qudit-Qubit Systems and Steerability-Entanglement in Qubit-Qudit Systems
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• Simple and maximally robust processes with no classical common-cause or direct-cause explanation
• Exact Steering Bound for Two-Qubit Werner States
• Measurement compatibility in Bell nonlocality tests
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• EPR Steering inequalities with Communication Assistance
• Quantum steering with positive operator valued measures
• Geometric Steering Criterion for Two-qubit States
• Activation of nonlocality in bound entanglement
• Hierarchy of Genuine Multipartite Quantum Correlations
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Single-copy activation of Bell nonlocality via broadcasting of quantum states
• Optimal tests of genuine multipartite nonlocality
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Nonlocality activation in a photonic quantum network
• Experimental detection of steerability in Bell local states with two measurement settings
• Quantum steering of Bell-diagonal states with generalized measurements
• Shareability of steering in 2-producible states
• Necessary conditions for steerability of two qubits, from consideration of local operations
• Quantum cloning of steering
• Classical-hidden-variable description for entanglement dynamics of two-qubit pure states
• Local-hidden-state models for Bell diagonal states and beyond
• Detecting EPR steering via two classes of local measurements
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Keyring models: an approach to steerability
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Quantum conditional entropies and steerability of states with maximally mixed marginals
• Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator
• Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Environmental effects on nonlocal correlations
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole
• Locally inaccessible hidden quantum correlations
• Nonlocality of Quantum States can be Transitive
• Local-hidden-state models for T-states using finite shared randomness
• Constructing local models for general measurements on bosonic Gaussian states
• Better bounds on finite-order Grothendieck constants
• Certifying the activation of Bell nonlocality with finite data