Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

Ghosh, Sibasish; Kar, Guruprasad; Roy, Anirban; Sarkar, Debasis; Sen, Aditi; Sen, Ujjwal

doi:10.1103/physreva.65.062307

Cited by 41 publications

(35 citation statements)

References 19 publications

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“…It is this nonorthogonality that manifests itself in a more complex form in the examples of LOCC-indistinguishable orthogonal product bases [10,56,57]. More generally, it may be the reason for any case of LOCC-indistinguishability of orthogonal states [58,59,60,61,62].…”

Section: Zero-way and One-way Subclassesmentioning

confidence: 99%

Local versus nonlocal information in quantum-information theory: Formalism and phenomena

et al. 2005

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In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. It is important from both pragmatic and theoretical points of view to know relationships between the two components. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudo-classically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal i.e. has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other non-local phenomena which can be found using the paradigm of local information. For example, we prove the existence of a form of non-locality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal (and in fact can be thought of as quasi-nonlocalisable). We also show that there do not exist states, for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proven that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions. Contents

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Section: Zero-way and One-way Subclassesmentioning

confidence: 99%

Local versus nonlocal information in quantum-information theory: Formalism and phenomena

et al. 2005

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“…It consists in the so called square-root measurement that discriminates with minimum error between N equally probable symmetric states. Symmetric pure states are defined in such a way that each state results from its predecessor by applying a unitary operator V in a cyclic way [47], 75) implying that V N = I. For the case that the states occur with equal a priori probability, i. e. that η j = 1/N for each of the states, Ban et al found that the optimum detection operators for minimum-error discrimination are given by [47] 76) where…”

Section: Selected Problems Of Minimum-error Discrimination Distinguismentioning

confidence: 99%

“…Ghosh, et al have shown that it is not possible, in general, to deterministically distinguish either three or four orthogonal two-qubit states using only local operations and classical communication [75]. A general condition on when orthogonal, bipartite 2 × d states (one of the particles is a qubit and the other a qudit), can be distinguished by LOCC was found recently by Walgate and Hardy [76].…”

Section: Discriminating Multiparticle Statesmentioning

confidence: 99%

Discrimination of quantum states

Bergou

2010

Journal of Modern Optics

207

223

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Abstract. The problem of discriminating among given nonorthogonal quantum states is underlying many of the schemes that have been suggested for quantum communication and quantum computing. However, quantum mechanics puts severe limitations on our ability to determine the state of a quantum system. In particular, nonorthogonal states cannot be discriminated perfectly, even if they are known, and various strategies for optimum discrimination with respect to some appropriately chosen criteria have been developed. In this article we review recent theoretical progress regarding the two most important optimum discrimination strategies. We also give a detailed introduction with emphasis on the relevant concepts of the quantum theory of measurement. After a brief introduction into the field, the second chapter deals with optimum unambiguous, i. e error-free, discrimination. Ambiguous discrimination with minimum error is the subject of the third chapter. The fourth chapter is devoted to an overview of the recently emerging subfield of discriminating multiparticle states. We conclude with a brief outlook where we attempt to outline directions of research for the immediate future. IntroductionIn quantum information and quantum computing the carrier of information is some quantum system and information is encoded in its state [1]. The state, however, is not an observable in quantum mechanics [2] and, thus, a fundamental problem arises: after processing the information -i.e. after the desired transformation is performed on the input state by the quantum processor -the information has to be read out or, in other words, the state of the system has to be determined. When the possible target states are orthogonal, this is a relatively simple task if the set of possible states is known. But when the possible target states are not orthogonal they cannot be discriminated perfectly, and optimum discrimination with respect to some appropriately chosen criteria is far from being trivial even if the set of the possible nonorthogonal states is known. Thus the problem of discriminating among nonorthogonal states is ubiquitous in quantum information and quantum computing, underlying many of the communication and computing schemes that have been suggested so far. It is the purpose of this article to review various theoretical schemes that have been developed for discriminating among nonorthogonal quantum states. The corresponding experimental

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“…For example, Ghosh, et al have shown that it is not possible to deterministically distinguish either three or four orthogonal two-qubit states using only local operations and classical communication [12]. This suggests that there is much still to be learned about distinguishing multipartite states using local operations and classical communication.…”

Section: Resultsmentioning

confidence: 99%

Distinguishing two-qubit states using local measurements and restricted classical communication

Hillery

Mimih

2003

Phys. Rev. A

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The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties, Alice and Bob, are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure is the same as if the two particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party's measurement depends on the result of the other party's. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of these procedure, in particular to secret sharing, are discussed.

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Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

Cited by 41 publications

References 19 publications

Local versus nonlocal information in quantum-information theory: Formalism and phenomena

Local versus nonlocal information in quantum-information theory: Formalism and phenomena

Discrimination of quantum states

Distinguishing two-qubit states using local measurements and restricted classical communication

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