Quantum steering with positive operator valued measures

Nguyen, Hai-Chau; Milne, Antony; Thanh, Vu; Jevtic, Sania

doi:10.1088/1751-8121/aad115

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Quantum steering with positive operator valued measures

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Nguyen, Hai-Chau
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Nguyen, H.-C., Milne, A., Thanh, V., & Jevtic, S. (2018). Quantum steering with positive operator valued measures. Journal of Physics A, 51(35): 355302. doi:10.1088/1751-8121/aad115.

Cite as: https://hdl.handle.net/21.11116/0000-0001-F290-A

Abstract

We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of determining the steerability of a bipartite quantum state of finite dimension with POVMs can be formulated as a nesting problem of two convex objects. One consequence of this is the strengthening of the theorem that justifies choosing the LHS ensemble based on symmetry of the bipartite state. As a more practical application, we study the classic problem of the steerability of two-qubit Werner states with POVMs. We show strong numerical evidence that these states are unsteerable with POVMs up to a mixing probability of 1/2 within an accuracy of 10(-3).