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Quantum steering with positive operator valued measures. (English) Zbl 1397.81045

Summary: 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 \(\frac{1}{2}\) within an accuracy of \(10^{-3}\).

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
81P15 Quantum measurement theory, state operations, state preparations
46G10 Vector-valued measures and integration
81P05 General and philosophical questions in quantum theory

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