Minimum-error discrimination between mixed quantum states

Qiu, Daowen

doi:10.1103/physreva.77.012328

Cited by 61 publications

(55 citation statements)

References 48 publications

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“…, A r . In this section we review a lower bound on the optimal error probability for discriminating between r given states in terms of the optimal pairwise error probabilities, originally given in [45]. Let us thereto define the following quantities:…”

Section: Pairwise Discrimination and Lower Decoupling Boundsmentioning

confidence: 99%

“…In Appendix B we show how our approaches work in the classical case (when all operators commute), thus providing various alternative proofs for (5) in the classical case. In Appendix C we review the pure state case; we show an elementary way to derive the Chernoff bound theorem (4) for two pure states, and show how the combination of the singleshot bounds of [19] and [45] yield (5) for an arbitrary number of pure states. In Appendix D we review the dual formulation of the optimal error probability due to [53].…”

Section: Introductionmentioning

confidence: 99%

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Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

Audenaert

Mosonyi

2014

Journal of Mathematical Physics

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We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states σ 1 , . . . , σ r . By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesized that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(σ 1 , . . . , σ r ), as recently introduced by Nussbaum and Szko la in analogy with Salikhov's classical multi-hypothesis Chernoff bound. This quantity is defined as the minimum of the pairwise binary Chernoff divergences min j

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Section: Pairwise Discrimination and Lower Decoupling Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

Audenaert

Mosonyi

2014

Journal of Mathematical Physics

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“…Because of the equal overlap between our input states, the minimum error rate for MESD in d dimensions [43,49] reduces to…”

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confidence: 99%

Discriminating Single-Photon States Unambiguously in High Dimensions

et al. 2014

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The ability to uniquely identify a quantum state is integral to quantum science, but for nonorthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the nondeterministic protocol of unambiguous state discrimination enables the error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between nonorthogonal, high-dimensional states encoded in single photons; our results range from dimension d=2 to d=14. We quantify the performance of our method by comparing the total measured error rate to the theoretical rate predicted by minimum-error state discrimination. For the chosen states, we find a lower error rate by more than 1 standard deviation for dimensions up to d=12. This method will find immediate application in high-dimensional implementations of quantum information protocols, such as quantum cryptography.

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“…Optimal measurements for group-covariant state sets have been well investigated, and it has been derived that a G-covariant optimal measurement exists for a G-covariant state set under several optimality criteria [5-8,17,23,36,38,39]. These results not only help us to obtain analytical optimal solutions (e.g., [40][41][42]), but also are useful for developing computationally efficient algorithms for obtaining optimal solutions [43,44]. In this section, we generalize these results to our generalized optimization problems.…”

Section: Group Covariant Optimization Problemmentioning

confidence: 96%

Generalized quantum state discrimination problems

2015

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We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a fixed rate of inconclusive results. Our approach can deal with any problem in which each of the objective and constraint functions is formulated by the sum of the traces of the multiplication of a Hermitian operator and a detection operator. We first derive dual problems and necessary and sufficient conditions for an optimal measurement. We also consider the minimax version of these problems and provide necessary and sufficient conditions for a minimax solution. Finally, for optimization problem having a certain symmetry, there exists an optimal solution with the same symmetry. Examples are shown to illustrate how our results can be used

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Minimum-error discrimination between mixed quantum states

Cited by 61 publications

References 48 publications

Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination

Discriminating Single-Photon States Unambiguously in High Dimensions

Generalized quantum state discrimination problems

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