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.
Highlights
The difficulty in understanding the explicit dependence of prior probability in nonlocality without entanglement” (NLWE) is due to the fact that a general method to obtain an optimal measurement for three quantum states is not known yet
In understanding this problem, one can recall a result obtained by Walgate and Hardy[5]. It tells that in a two-qubit system, three pure orthogonal states can be perfectly discriminated by a finite-round local operations and classical communication (LOCC) if and only if at least two of them are product states. It means that fjΦii hΦijg2i1⁄40 can be perfectly discriminated by a finite-round LOCC if and only if at least two possibility entangled of fjΦii hΦijg2i1⁄40 are of NLWE depends or not
In this study, we showed that nonlocality depends on γ0 1⁄4 cos 2εð[1] þ sin 2εÞ: separable quantum states of a quantum ensemble and the (11) prior probabilities of given quantum states
Summary
In 1991, Peres and Wootters proposed a seminal problem[1]: What is the difference between global and local measurements on quantum states prepared at different locations? The question naturally leads to an investigation into the role of local operations and classical communication (LOCC), which is necessary for characterizing entanglement[2] and the nonlocality of quantum information[3,4,5,6,7,8,9,10,11,12,13,14,15]. Because the global measurement is to measure quantum states at different locations as a whole, it can be entangled or not. When it is not entangled, it is called a separable measurement (SEP). A local measurement is to measure locally quantum states at different locations. Every LOCC can be realized through SEP, but the inverse does not hold[3]
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