Local Hidden Variable Theories for Quantum States

Abstract

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasi-extension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.

8 pages Revtex; v2 contains substantial changes, a strengthened main theorem and more references

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Cited by in corpus (71)

• Bell nonlocality
• Entanglement detection
• Matrix product states represent ground states faithfully
• Quantum cloning
• A complete family of separability criteria
• General properties of Nonsignaling Theories
• Quantifying Einstein-Podolsky-Rosen steering
• Device-independent witnesses of genuine multipartite entanglement
• Spin squeezing and entanglement
• Joint measurability of generalized measurements implies classicality
• Grothendieck's constant and local models for noisy entangled quantum states
• Monogamy of nonlocal quantum correlations
• One-and-a-half quantum de Finetti theorems
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• Detecting multipartite entanglement
• Evaluation of convex roof entanglement measures
• Comments on Entanglement Negativity in Holographic Field Theories
• Monogamy of Correlations vs. Monogamy of Entanglement
• Monogamy of Bell's inequality violations in non-signaling theories
• Algorithmic construction of local hidden variable models for entangled quantum states
• Optimal probabilistic cloning and purification of quantum states
• Genuine three-partite entangled states with a local hidden variable model
• Bounds on Quantum Correlations in Bell Inequality Experiments
• Activation of Non-Local Quantum Resources
• On quantum advantage in dense coding
• Gaussian quantum marginal problem
• On the local and non-local content of bipartite qubit and qutrit correlations
• Fundamental limits on key rates in device-independent quantum key distribution
• Symmetric Extension of Two-Qubit States
• Type-independent Characterization of Spacelike Separated Resources
• All entangled states display some hidden nonlocality
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Nonlocality tests enhanced by a third observer
• Nonviolation of Bell's Inequality in Translation Invariant Systems
• Persistency of entanglement and nonlocality in multipartite quantum systems
• Local Realism of Macroscopic Correlations
• One-way quantum key distribution: Simple upper bound on the secret key rate
• Symmetric extension in two-way quantum key distribution
• Finite de Finetti theorem for conditional probability distributions describing physical theories
• Designing Quantum Information Processing via Structural Physical Approximation
• Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
• Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
• Extendibility of bosonic Gaussian states
• Activation of monogamy in non-locality using local contextuality
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually
• Simple test for quantum channel capacity
• Incompatible local hidden-variable models of quantum correlations
• Truncated su(2) moment problem for spin and polarization states
• Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing
• Bounding the persistency of the nonlocality of W states
• Class of bipartite quantum states satisfying the original Bell inequality
• Decoherence-Free Emergence of Macroscopic Local Realism for entangled photons in a cavity
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• On single-photon quantum key distribution in the presence of loss
• Generalizing optimal Bell inequalities
• Symmetric extendibility for a class of qudit states
• Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space
• Quantifying the unextendibility of entanglement
• Symmetric extendibility of quantum states
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• Experimental single-copy distillation of quantumness from higher-dimensional entanglement
• On Exchangeable Continuous Variable Systems
• Distilling multipartite pure states from a finite number of copies of multipartite mixed states
• Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Nonlocality of Quantum States can be Transitive
• Investigation of nonlocal information as condition for violations of Bell inequality and information causality
• Monogamy of highly symmetric states
• Full Bell locality of a noisy state for $N\ge 3$ nonlocally entangled qudits
• Robust Multipartite Entanglement Without Entanglement Breaking