Erratum: Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions [Phys. Rev. A 72, 022342 (2005)]

Raynal, Philippe; Lütkenhaus, Norbert

doi:10.1103/physreva.72.049909

Cited by 13 publications

(45 citation statements)

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“…(23) implies vectors C and X are in the same direction, which immediately leads to the symmetry of Eq. (21). Equality of inequality (24) requires the relation of Eq.…”

Section: Intermediate Domainmentioning

confidence: 99%

Discrimination with error margin between two states: Case of general occurrence probabilities

et al. 2009

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We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.

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“…(23) implies vectors C and X are in the same direction, which immediately leads to the symmetry of Eq. (21). Equality of inequality (24) requires the relation of Eq.…”

Section: Intermediate Domainmentioning

confidence: 99%

Discrimination with error margin between two states: Case of general occurrence probabilities

et al. 2009

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“…3) through USD, the measurement scheme becomes less practical involving photon number resolving detectors [29]. The USD of mixed quantum states is a much more subtle issue than that of pure states [30,31,32,33]. Nonetheless, for equal a priori probabilities (which is the FIG.…”

Section: Ultimate Boundsmentioning

confidence: 99%

“…case we are interested in), the failure probability (the probability for obtaining an inconclusive measurement outcome) is bounded from below by the square root of the fidelity of the two density operators [32]. For the USD problem of Eq.…”

Section: Ultimate Boundsmentioning

confidence: 99%

Quantum repeaters using coherent-state communication

et al. 2008

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We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.

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“…This analysis can be applied for the unambiguous discrimination of any two density operators acting on a Hilbert space up to dimensions five. This goes beyond previous results which require a high symmetry or other very special properties of the given states [7][8][9][10][11][12][13]. We will show the main ideas and steps towards the solution, and explain the technical details elsewhere [14].…”

mentioning

confidence: 79%

“…Furthermore, in Ref. [11] the importance of unambiguous discrimination in the context of quantum key distribution was shown with particular emphasis on the case of states of rank two. As an outlook, our strategy seems a promising path for the generalization to unambiguous state discrimination of more than two states.…”

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confidence: 99%

Unambiguous discrimination of mixed quantum states: Optimal solution and case study

2010

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We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space dimensions smaller or equal to five this leads to the complete optimal solution. We demonstrate our method with a physical example, namely the unambiguous comparison of n quantum states, and find the optimal success probability. PACS numbers: 03.67.-a,03.65.TaAccording to the laws of quantum mechanics, two nonorthogonal quantum states cannot be distinguished perfectly. This fact has far-reaching consequences in quantum information processing, e.g. it allows to generate a secret random key in quantum cryptography. In spite of the fundamental nature of the problem of state discrimination, determining the optimal measurement to distinguish two (mixed) quantum states is far from being trivial.In the literature, two main paths to state discrimination have been taken [1]: firstly, in minimum error discrimination, the unavoidable error in distinguishing two states from each other is minimized. This problem has been completely solved in Ref. [2]. Secondly, in unambiguous state discrimination (USD), no error is allowed, but an inconclusive answer may occur. The optimal USD measurement minimizes the probability of an inconclusive answer [3][4][5]. Although USD has found much attention in the recent years, and special examples have been solved, no general solution is known so far for the case of mixed states. A strategy that is analogous to USD, but applicable also for linearly dependent states are maximum confidence measurements, discussed in Ref. [6].The aim of the current contribution is to present the optimal USD measurement for cases which cannot be reduced to the pure state case and thus to known solutions. This analysis can be applied for the unambiguous discrimination of any two density operators acting on a Hilbert space up to dimensions five. This goes beyond previous results which require a high symmetry or other very special properties of the given states [7][8][9][10][11][12][13]. We will show the main ideas and steps towards the solution, and explain the technical details elsewhere [14].The scenario of optimal unambiguous discrimination of two density operators is as follows: two (normalized) density operators ̺ 1 and ̺ 2 , acting on a finite-dimensional Hilbert space H occur with a priori probability p 1 and p 2 , respectively, where p 1 + p 2 = 1. We will denote * Electronic address: Matthias.Kleinmann@uibk.ac.at the support of a density operator ̺ as the orthocomplement of its kernel, (supp ̺) ⊥ = ker ̺. A measurement for USD is described by a positive operator valued measure (POVM), i.e., a family of positive semi-definite operators {E 1 , E 2 , E ? } with E 1 + E 2 + E ? = 1 1, obeying the constraints for unambiguity, tr(E 2 ̺ 1 ) = 0 and tr(E 1 ̺ 2 ) = 0. The operator E ? corresponds to the inconclusive outcome while E 1 and E 2 correspond to the successful detection of ̺ 1 ...

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Erratum: Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions [Phys. Rev. A 72, 022342 (2005)]

Cited by 13 publications

References 0 publications

Discrimination with error margin between two states: Case of general occurrence probabilities

Discrimination with error margin between two states: Case of general occurrence probabilities

Quantum repeaters using coherent-state communication

Unambiguous discrimination of mixed quantum states: Optimal solution and case study

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