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The European Physical Journal D

Splitting four ensembles of two-qubit quantum information via three Einstein-Podolsky-Rosen pairs

W. Zhang, Y. M. Liu, Xu-Fei Yin, Z. J. Zhang

Published Jun 17, 2009• 18 citations
Publisher
DOI
10.1140/epjd/e2009-00180-y

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Quantum nonlocality is an essential resource in quantum information and is commonly classified into three distinct forms: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Gisin's theorem shows that pure-state entanglement implies Bell nonlocality, and it motivates the question of how entanglement and EPR steering are related beyond pure states. Here we prove that every entangled rank-2 two-qubit state is EPR steerable, with rank-1 states included as a special case. The proof combines a local-unitary parametrization of rank-2 two-qubit states, a necessary and sufficient separability condition, and a state-dependent nonlinear steering inequality. This gives an analytical characterization of EPR steerability for rank-2 two-qubit entangled states. Thus, rank-2 two-qubit entangled states provide certifiable EPR-steering resources in quantum information.