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Optimal Unambiguous Discrimination and Nonlocality without Entanglement

Donghoon Ha, Jeong San Kim

Published May 26, 2021• 0 citations
OpenAlex

Abstract

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. Recently, it has been found that NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, 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.

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Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. Recently, it has been found that NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, 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.
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.
Abstract The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus it is natrual to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination stratigies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurence of NLWE in terms of optimal nambiguous discrimination. Our results can provide a useful application for hiding or sharing information based on non-orthogonal separable states.
The phenomenon of nonlocality without entanglement (NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus It is natural to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination strategies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurrence of NLWE in terms of optimal unambiguous discrimination. Our results can provide a useful application for hiding or sharing information based on non-orthogonal separable states.
Nonlocality without entanglement (NLWE) is a nonlocal quantum phenomenon that arises in separable state discrimination. We show that the availability of the postmeasurement information about the prepared subensemble can affect the occurrence of NLWE in discriminating non-orthogonal nonentangled states. We provide a two-qubit state ensemble consisting of four nonorthogonal separable pure states and show that the postmeasurement information about the prepared subensemble can annihilate NLWE. We also provide another two-qubit state ensemble consisting of four nonorthogonal separable states and show that the postmeasurement information can create NLWE. Our result can provide a useful method to share or hide information using nonorthogonal separable states.
An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.
In this work, we present the framework for demonstrating and certifying the distinction between measurements in an entangled basis, called global measurements, and local operations and classical communication (LOCC), known as nonlocality without entanglement (NLWE). To be precise, we show NLWE via a maximum-confidence measurement in terms of a guess per detection event, called a confidence, a fine-grained guessing probability that encompasses both minimum-error and unambiguous state-discrimination strategies. We show that NLWE for unknown measurements can be certified, given the measurement-outcome rates, by bounding the confidence using LOCC; the certification is semi-device-independent in that state preparation is trusted. We illustrate the demonstration and certification of NLWE for antiparallel qubit states. Our results make it feasible to experimentally realize NLWE using measurement devices with imperfections, such as non-unit detection efficiency, since maximum-confidence measurements rely only on detected events.