Optimal local discrimination of two multipartite pure states

Virmani, S.; Sacchi, Massimiliano F.; Plenio, Martin B.; Markham, Damian

doi:10.1016/s0375-9601(01)00484-4

Cited by 175 publications

(166 citation statements)

References 21 publications

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“…Non-orthogonal bipartite and multipartite states have been considered with respect to both minimum-error discrimination and optimum unambiguous discrimination [6 -9]. It has been found [6] that any two pure non-orthogonal multipartite states can be discriminated with minimum error using only local measurements and classical communication, and that the same holds true for two mixed states provided these states span collectively only a two-dimensional Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Minimum-error discrimination between a pure and a mixed two-qubit state

Herzog

2004

J. Opt. B: Quantum Semiclass. Opt.

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The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability of errors in deciding whether the state of a quantum system is either a given pure state or a uniform statistical mixture of any number of mutually orthogonal states. The result is applied to two-qubit states, and the minimum error probabilities achievable by collective and local measurements on the qubits are compared.

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Section: Introductionmentioning

confidence: 99%

Minimum-error discrimination between a pure and a mixed two-qubit state

Herzog

2004

J. Opt. B: Quantum Semiclass. Opt.

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“…Later, Walgate et al proved that any two pure orthogonal states in finitedimensional systems can be distinguished with certainty using local operations and one-way classical communication (one-way LOCC) no matter how entangled they are [2]. These results encourage further investigations on the distinguishability of quantum states by LOCC, and several important results have been reported in the case of orthogonal states [3][4][5][6][7][8]. In this paper, we consider only finite-dimensional systems.…”

Section: Introductionmentioning

confidence: 66%

Realizing a 2-D Positive Operator-Valued Measure by Local Operations and Classical Communication

Nakahira¹,

Usuda²

2018

IEEE Trans. Inform. Theory

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We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a twodimensional Hilbert space in which each party's space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.

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“…These states are locally distinguishable if there are some sequence of local operations and classical communication (LOCC) by which Alice, Bob and Charles et al can always determine which state they own. There are many interesting works on the local distinguishability of orthogonal states [6][7][8][9][10][11][12][13][14][15]. These works improve our understanding on nonlocality.…”

Section: Introductionmentioning

confidence: 99%

Distinguishing the elements of a full product basis set needs only projective measurements and classical communication

Chen

2004

Phys. Rev. A

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Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the local indistinguishability of a set of orthogonal product states. In this paper we analyze the character of operators to distinguish a set of full product bases in a multi-partite system, and show that distinguishing perfectly a set of full product bases needs only local projective measurements and classical communication, and these measurements cannot damage each product basis. Employing these conclusions one can discuss local distinguishability of full product bases easily. Finally we discuss the generalization of these results to the locally distinguishability of a set of incomplete product bases. PACS number(s): 89.70.+c, 03.65.ud Typeset using REVT E X * E-mail: pxchen@nudt.edu.cn 1 An important manifestation of quantum nonlocality is entanglement [1]. The entangled states can be used for novel forms of information processing, such as quantum cryptography [2,3], quantum teleportation [4], and fast quantum computation [5]. However, there also exists nonlocality in inentangled states [6,7], even in a state of a particle [3]. This is known as nonlocality without entanglement. The protocols of single photon cryptography [3] are examples which uses the nonlocality without entanglement. The nonlocality without entanglement may be an important field just as the entanglement. Closely related to the nonlocality without entanglement is the local distinguishability of a set of inentangled states [6,7].Alice, Bob and Charles et al share a quantum system, in one of a known set of possible orthogonal states. They do not, however, know which state they have. These states are locally distinguishable if there are some sequence of local operations and classical communication (LOCC) by which Alice, Bob and Charles et al can always determine which state they own. There are many interesting works on the local distinguishability of orthogonal states [6][7][8][9][10][11][12][13][14][15]. These works improve our understanding on nonlocality. The discussion on the local distinguishability of orthogonal product states (OPSs) may enlarge our acknowledge of nonlocality without entanglement. Bennett et al first [6] showed that there are 9 OPSs in a 3 ⊗ 3 system which are indistinguishable by LOCC. Walgate et al [7] provide a more simple proof of indistinguishability of the Bennett's 9 OPSs. However few papers discussed the local distinguishability of more general OPSs in a multi-partite system. This paper will focus on the local distinguishability of a set of complete OPSs {|Ψ k } in a multi-partite system. We will show that a set of full OPSs are LOCC perfectly distinguishable if and only if these OPSs are distinguishable by projective measurements and classical communication, and these measurements cannot damage each state |Ψ k . Using this result we can prove easily that the Bennett's 9 OPSs [6] are indistinguishable by LOCC, and can provide many new sets of locally indistinguishable OPSs in multi-p...

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Optimal local discrimination of two multipartite pure states

Cited by 175 publications

References 21 publications

Minimum-error discrimination between a pure and a mixed two-qubit state

Minimum-error discrimination between a pure and a mixed two-qubit state

Realizing a 2-D Positive Operator-Valued Measure by Local Operations and Classical Communication

Distinguishing the elements of a full product basis set needs only projective measurements and classical communication

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