Quantum channels transforming Bell local states as unsteerable states

Abstract

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.

Perfect NOT and conjugate transformations

“…Of course, unitary operation and measurement are extensively used in quantum key distribution [21]. It is also used in quantum steering [22]. As for preparation of quantum state, two examples are given in refs.…”