Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
arXiv:1601.00962 · doi:10.1103/PhysRevA.95.062111
Abstract
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable-local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal full correlations (excluding marginal statistics) in this scenario if and only if it can generate Bell-nonlocal correlations. If full statistics (including marginal statistics) is taken into account, surprisingly, the same scenario can manifest the simplest one-way steering and the strongest hierarchy between steering and Bell nonlocality. To illustrate these intriguing phenomena in simple setups, several concrete examples are discussed in detail, which facilitates experimental demonstration. In the course of study, we introduce the concept of restricted LHS models and thereby derive a necessary and sufficient semidefinite-programming criterion to determine the steerability of any bipartite state under given measurements. Analytical criteria are further derived in several scenarios of strong theoretical and experimental interest.
New results added, 13 pages, 3 figures; published in Phys. Rev. A
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Cited by in corpus (13)
- Quantum Steering
- Experimental hierarchy of two-qubit quantum correlations without state tomography
- Einstein-Podolsky-Rosen Steering Criterion and Monogamy Relation via Correlation Matrices in Tripartite Systems
- Shareability of steering in 2-producible states
- On the power of one pure steered state for EPR-steering with a pair of qubits
- Experimental Verification of Anisotropic Invariance for Three-Qubit States
- Detecting the genuine multipartite two-way steerability with linear steering inequalities
- Diagnosing steerability of a bipartite state with the nonsteering threshold
- Averaged fidelity-based steering criteria
- Hidden Bell correlations in the four-level atom
- Manipulating the direction of one-way steering in an optomechanical ring cavity
- Parameterized steering criteria via correlation matrices
- Imprecise quantum steering inequalities in tripartite systems