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

Hillery, Mark; Mimih, Jihane

doi:10.1103/physreva.67.042304

Cited by 25 publications

(22 citation statements)

References 14 publications

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“…Together with Mimih we took a somewhat different approach to unambiguous discrimination of two-qubit states [70]. The motivation was to study bipartite state discrimination schemes that could be used in quantum communication protocols, quantum secret sharing, in particular [71]- [74].…”

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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Section: Discriminating Multiparticle Statesmentioning

confidence: 99%

Discrimination of quantum states

Bergou

2010

Journal of Modern Optics

207

223

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“…In a previous paper we discussed such a scheme. 10 In it, both parties measure their qubit immediately upon receiving it, each obtaining a result of either 0 or 1. There are four sets of results: {0, 0}, {1, 1},{0, 1}, and {1, 0}.…”

Section: Introductionmentioning

confidence: 99%

Unambiguous discrimination of two nonorthogonal multipartite states using local measurements and classical communication (Invited Paper)

Mimih

Hillery

2005

SPIE Proceedings

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We consider a quantum system of two nonorthogonal bipartite states, |Ψ 0 and|Ψ 1 . We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.

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“…Therefore, we cannot construct a POVM that is error-free, and for which Alice and Bob receive simultaneous failure signals, when the procedure fails. It should be noted, as shown in [10], that if qutrits are used instead of qubits, an error-free POVM with simultaneous failure signals is possible.…”

Section: Failure Indication Received By Both Partiesmentioning

confidence: 99%

“…In a previous paper we discussed such a scheme [10]. In it, both parties measure their qubit immediately upon receiving it, each obtaining a result of either 0 or 1.…”

Section: Introductionmentioning

confidence: 99%

Unambiguous discrimination of special sets of multipartite states using local measurements and classical communication

Mimih

Hillery

2005

Phys. Rev. A

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We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, |Ψ0 and|Ψ1 . We distribute the qubits to two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability that would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit, and qudit, states. Applications to quantum secret sharing are discussed. Finally, we present an optical scheme to experimentally realize the protocol in the case of two qubits.

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

Cited by 25 publications

References 14 publications

Discrimination of quantum states

Discrimination of quantum states

Unambiguous discrimination of two nonorthogonal multipartite states using local measurements and classical communication (Invited Paper)

Unambiguous discrimination of special sets of multipartite states using local measurements and classical communication

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