Optimal quantum violation of Clauser-Horne-Shimony-Holt like steering inequality

Abstract

We study a recently proposed Einstein-Podolsky-Rosen steering inequality [arXiv- 1412.8178 (2014)]. Analogous to Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell nonlocality, in the simplest scenario, i.e., 2 parties, 2 measurements per party and 2 outcomes per measurement, this newly proposed inequality has been proved to be necessary and sufficient for steering. In this article, using an equivalence between measurement incompatibility (non joint measurability) and steering, we find the optimal violation amount of this inequality in quantum theory. Interestingly, the optimal violation amount matches with optimal quantum violation of CHSH inequality, i.e., Cirel'son quantity. We further study the optimal violation of this inequality for different bipartite quantum states. To our surprise we find that optimal violation amount is different for different $2$-qubit pure entangled states, which is not the case for all other existing steering inequalities.

5.5 pages, 2 figures, Comments are welcome

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Cited by in corpus (7)

• Quantification of Einstein-Podolski-Rosen steering for two-qubit states
• All two-qubit states that are steerable via Clauser-Horne-Shimony-Holt-type correlations are Bell nonlocal
• Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Entanglement Dynamics for Two Spins in an Optical Cavity---Field Interaction Induced Decoherence and Coherence Revival
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Detecting EPR steering via two classes of local measurements