All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal

Abstract

We derive a new inequality that is necessary and sufficient to show EPR-steering in a scenario employing only correlations between two arbitrary dichotomic measurements on each party. Thus the inequality is a complete steering analogy of the CHSH inequality, a generalisation of the result of Cavalcanti et al, JOSA B, 32(4), A74 (2015). We show that violation of the inequality only requires measuring over equivalence classes of mutually unbiased measurements on the trusted party and in fact assuming a general two qubit system arbitrary pairs of distinct projective measurements at the trusted party are equally useful. Via this it is found that for a given state the maximum violation of our EPR-steering inequality is equal to that for the CHSH inequality, so all states that are EPR-steerable with CHSH-type correlations are also Bell nonlocal.

5+4 pages. V2: close to journal version, simpler proof of steering inequality, examine dichotomic POVM case

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Cited by in corpus (26)

• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Anisotropic invariance and the distribution of quantum correlations
• Revealing of hidden quantum steerability using local filtering operations
• Detecting Einstein-Podolsky-Rosen steering through entanglement detection
• Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
• Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States
• Enhancement of cooperation by giving high-degree neighbors more help
• Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
• Reference frame independent Einstein-Podolsky-Rosen steering
• Creating quantum correlations in generalized entanglement swapping
• Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements
• Shareability of steering in 2-producible states
• Detecting EPR steering via two classes of local measurements
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Detecting the genuine multipartite two-way steerability with linear steering inequalities
• Experimental Verification of Anisotropic Invariance for Three-Qubit States
• Role of maximally entangled states in the context of linear steering inequalities
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Averaged fidelity-based steering criteria
• Parameterized steering criteria via correlation matrices
• Imprecise quantum steering inequalities in tripartite systems