Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination

Abstract

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination.

Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states

“…( 47 ). It is known that an unambiguous measurement is optimal if and only if there is a positive-semidefinite operator K satisfying the following condition 21 , 43 – 45 , In this case, we have if an unambiguous measurement and a positive-semidefinite operator K satisfy Condition ( 49 ) 21 , 43 – 45 .…”

“…In the case of discriminating orthogonal non-entangled states, NLWE occurs when the perfect discrimination cannot be implemented by LOCC 5 – 9 . On the other hand, in the case of discriminating non-orthogonal non-entangled states, NLWE occurs when the globally optimal discriminations such as minimum-error discrimination 10 – 13 or optimal unambiguous discrimination 14 – 17 cannot be implemented by LOCC 18 – 21 . We also note that some non-local phenomena without entanglement can occur in the generalized probabilistic theories beyond quantum theory 22 .…”

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

“…According to a recent investigation, the selection of prior probability can affect the quantum properties of the system [ 36 , 37 ]. Therefore, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states when the MED of two pure quantum states with arbitrary prior probabilities is considered.…”