Orthogonal quantum states can be unambiguously distinguished by local measurements.
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Peer-reviewed literature demonstrates that orthogonal quantum states cannot always be distinguished perfectly or unambiguously by local operations and classical communication.
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.
We study the distinguishability of bipartite quantum states by Positive Operator-Valued Measures with positive partial transpose (PPT POVMs). The contributions of this paper include: (1). We give a negative answer to an open problem of [M. Horodecki $et. al$, Phys. Rev. Lett. 90, 047902(2003)] showing a limitation of their method for detecting nondistinguishability. (2). We show that a maximally entangled state and its orthogonal complement, no matter how many copies are supplied, can not be distinguished by PPT POVMs, even unambiguously. This result is much stronger than the previous known ones \cite{DUAN06,BAN11}. (3). We study the entanglement cost of distinguishing quantum states. It is proved that $\sqrt{2/3}\ket{00}+\sqrt{1/3}\ket{11}$ is sufficient and necessary for distinguishing three Bell states by PPT POVMs. An upper bound of entanglement cost of distinguishing a $d\otimes d$ pure state and its orthogonal complement is obtained for separable operations. Based on this bound, we are able to construct two orthogonal quantum states which cannot be distinguished unambiguously by separable POVMs, but finite copies would make them perfectly distinguishable by LOCC. We further observe that a two-qubit maximally entangled state is always enough for distinguishing a $d\otimes d$ pure state and its orthogonal complement by PPT POVMs, no matter the value of $d$. In sharp contrast, an entangled state with Schmidt number at least $d$ is always needed for distinguishing such two
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