Experimental optimal maximum-confidence discrimination and optimal unambiguous discrimination of two mixed single-photon states

Steudle, Gesine A.; Knauer, Sebastian; Herzog, Ulrike; Stock, E.; Haisler, V. A.; Bimberg, D.; Benson, Oliver

doi:10.1103/physreva.83.050304

Cited by 14 publications

(10 citation statements)

References 25 publications

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“…When unambiguous discrimination is impossible, related measurements can be applied, which discriminate the states with maximum possible confidence for each conclusive outcome [16,17]. Optimized maximum-confidence discrimination is achieved by the particular one of these measurements that minimizes the failure probability [18][19][20][21][22]. This measurement corresponds to optimum unambiguous discrimination when for each of the different conclusive results the maximum confidence is equal to unity.…”

Section: Introductionmentioning

confidence: 99%

Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate

Herzog¹

2012

Phys. Rev. A

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We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error discrimination if this value is zero, while under certain conditions it corresponds to optimized maximum-confidence discrimination, or to optimum unambiguous discrimination, respectively, when the fixed value reaches a definite minimum. Using operator conditions that determine the optimum measurement, we derive analytical solutions for the discrimination of two mixed qubit states, including the case of two pure states occurring with arbitrary prior probabilities, and for the discrimination of N symmetric states, both pure and mixed. We also consider a case where the given density operators resolve the identity operator, and we specify the optimality conditions for partially symmetric states. Moreover, we show that from the complete solution for arbitrary values of the fixed rate of inconclusive results one can always obtain the optimum measurement in another strategy where the error rate is fixed, and vice versa.

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Section: Introductionmentioning

confidence: 99%

Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate

Herzog¹

2012

Phys. Rev. A

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“…The optimized maximum-confidence discrimination of two mixed qubit states has been theoretically investigated in our previous paper [21]. We also proposed an implementation of the optimum measurement [22], which has been recently experimentally realized for two mixed qubit states having the same purity [23].…”

Section: Introductionmentioning

confidence: 99%

Optimized maximum-confidence discrimination ofNmixed quantum states and application to symmetric states

Herzog

2012

Phys. Rev. A

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We study an optimized measurement which discriminates N mixed quantum states occurring with given prior probabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the overall probability of inconclusive outcomes as small as possible. It corresponds to optimum unambiguous discrimination when for each outcome the confidence is equal to unity. Necessary and sufficient optimality conditions are derived and general properties of the optimum measurement are obtained. The results are applied to the optimized maximum-confidence discrimination of N equiprobable symmetric mixed states. Analytical solutions are presented for a number of examples, including the discrimination of N symmetric pure states spanning a d-dimensional Hilbert space (d N ) and the discrimination of N symmetric mixed qubit states.

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“…A subsequent exper-iment with a similar source extended this to distinguish three states encoded in three-dimensional photon path information [31]. USD has also been performed for two mixed polarisation states using a quantum dot singlephoton source [32].…”

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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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Experimental optimal maximum-confidence discrimination and optimal unambiguous discrimination of two mixed single-photon states

Cited by 14 publications

References 25 publications

Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate

Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate

Optimized maximum-confidence discrimination ofNmixed quantum states and application to symmetric states

Discriminating Single-Photon States Unambiguously in High Dimensions

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