Quantum steering in tripartite quantum systems

Motivated by the contributions [Sci. Rep. 6, 39063 (2016)] and [Phys. Rev. A 98, 052114 (2018)], we aim to establish a new method for theoretically checking Bell nonlocality of a bipartite state of systems  A ⊗  B for any finite dimensional Hilbert spaces  A and  B , provided that the operator space B( B ) has an orthonormal basis consisting of the identity operator and Hermitian unitary operators. Our main result induces a quantum channel Φ T, transforming a Bell local state AB as an unsteerable state Φ T, ( AB ) from A to B whenever the parameters T and satisfy the condition Θ(T, ) ≤ 1. Thus, when Θ(T, ) ≤ 1 and the image Φ T, ( AB ) is steerable from Ato B, the original state AB must be Bell nonlocal. Our result not only reveals a deep connection between EPR steerability and Bell nonlocality but also provides a feasible approach to theoretically prove difficultly verified Bell nonlocality by translating it into easily verified steerability.

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Some Measurement-Based Characterizations of Separability of Bipartite States

Cao

Zhang

Guo

2021

Int J Theor Phys

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Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

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Quantum steering in tripartite quantum systems

Cited by 4 publications

References 23 publications

Detecting ${\boldsymbol~A}{\boldsymbol~B}{\boldsymbol~\rightarrow}{\boldsymbol~C}$ steering in tripartite quantum systems

Detecting ${\boldsymbol~A}{\boldsymbol~B}{\boldsymbol~\rightarrow}{\boldsymbol~C}$ steering in tripartite quantum systems

Quantum channels transforming Bell local states as unsteerable states

Some Measurement-Based Characterizations of Separability of Bipartite States

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