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arXiv:2405.20586 · Scientific Reports

Entanglement witness and nonlocality in confidence of measurement from multipartite quantum state discrimination

Donghoon Ha, Jeong San Kim

Published Oct 11, 2024• 2 citations
arXivHTMLPDF

Abstract

We consider multipartite quantum state discrimination and provide a specific relation between the properties of entanglement witness and quantum nonlocality inherent in the confidence of measurement. We first provide the definition of the confidence of measurement as well as its useful properties for various types of multipartite measurement. We show that globally-maximum confidence that cannot be achieved by local operations and classical communication strongly depends on the existence of a certain type of entanglement witness. We also provide conditions for an upper bound on maximum of locally-achievable confidence. Finally, we establish a method in terms of entanglement witness to construct quantum state ensembles with nonlocal maximum confidence.

DOI
10.1038/s41598-024-75149-y

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We consider multipartite quantum state discrimination and provide a specific relation between the properties of entanglement witness and quantum nonlocality inherent in the confidence of measurement. We first provide the definition of the confidence of measurement as well as its useful properties for various types of multipartite measurement. We show that globally-maximum confidence that cannot be achieved by local operations and classical communication strongly depends on the existence of a certain type of entanglement witness. We also provide conditions for an upper bound on maximum of locally-achievable confidence. Finally, we establish a method in terms of entanglement witness to construct quantum state ensembles with nonlocal maximum confidence.
Abstract We consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness (EW). Based on the properties of EW, we establish some necessary and/or sufficient conditions on minimum-error discrimination by separable measurements. We also provide some conditions on the upper bound of the maximum success probability over all possible separable measurements. Our results are illustrated by examples of multidimensional multipartite quantum states. Finally, we provide a systematic way in terms of the EW to construct multipartite quantum state ensembles showing nonlocality in state discrimination.
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.
Abstract In the case of a multi-party system, through local operations and classical communication (LOCC), each party may not perform perfect discrimination of quantum states that are separable and orthogonal. This property of quantum ensemble is called “nonlocality without entanglement” since each local party has a limit to full information of given quantum states. When this property is extended to the case of minimum-error discrimination, one can see that it is revealed when a nonlocal measurement provides more information about the unentangled states than LOCC does. One may infer the fact that the property depends on quantum states composing the quantum ensemble. However, an essential but unsettled question about the property is whether an explicit dependence on prior probabilities in terms of minimum-error discrimination could be shown in nonlocality without entanglement. In a simple term, one can ask whether different quantum ensembles made of the same separable quantum states could exhibit explicitly different behavior of the nonlocality. We answer this question in the positive, and we furthermore provide the explicit functional dependence of guessing probability on prior probabilities for the mirror-symmetric ensemble.
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.
Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical features of quantum theory. A variant of this phenomenon arises in conclusive local state discrimination, where the correct state must be identified with zero error, albeit allowing for inconclusive outcomes. More recently, the notion of local state marking has been introduced, with the focus shifted to correctly identifying the permutation of a subset of states randomly chosen from a given set of multipartite states under LOCC. In this work, we unify these two approaches by introducing the task of conclusive local state marking, which reveals a finer hierarchy of nonlocality in multipartite quantum state ensembles. Notably, we demonstrate that certain ensembles of product states can exhibit a stronger form of nonlocality than entangled ensembles traditionally considered highly nonlocal.
We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the concept of decomposable entanglement witness, we establish conditions on minimum-error discrimination by positive-partial-transpose measurements. We also provide conditions on the upper bound of the maximum success probability over all possible positive-partial-transpose measurements. Finally, we illustrate our results using examples of multidimensional bipartite quantum states.