Unambiguous discrimination of mixed states

Rudolph, Terry; Spekkens, Robert W.; Turner, Peter S.

doi:10.1103/physreva.68.010301

Cited by 137 publications

(186 citation statements)

References 17 publications

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“…For mixed states, it was shown in Ref. [22] that Eq. (2) can be satisfied if and only if one of the density operators i has a nonzero overlap with the intersection of the kernels of the other density operators.…”

Section: Problem Formulationmentioning

confidence: 99%

“…As noted in Ref. [22], by choosing an appropriate basis for B, the problem of maximizing P D subject to Eq. (8) can be put in the form of a standard semidefinite programming problem, which is a convex optimization problem; for a detailed treatment of semidefinite programming problems see, e.g., Refs.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Rudolph, Speakkens, and Turner [22] showed that unambiguous detection between mixed quantum states is possible as long as one of the density operators in the ensemble has a nonzero overlap with the intersection of the kernels of the other density operators. They then consider the problem of unambiguous detection between two mixed quantum states, and derive upper and lower bounds on the probability of an inconclusive result.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal quantum detectors for unambiguous detection of mixed states

2004

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We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that minimizes the probability of an inconclusive result. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal quantum detectors for unambiguous detection of mixed states

2004

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“…It is stressed again that the cost of our testing scenario does not include the prior probabilities of the signals. We also note that the pure state filtering scenarios with Bayesian hypothesis testing have been discussed in context of minimum-error and unambiguous discriminations of quantum signal subsets [7,8], and the latter one was recently recasted by the more general theory of mixed state unambiguous discrimination [9].…”

Section: Introductionmentioning

confidence: 99%

“…Since quantum mechanics does not allow us to discriminate non-commutative states perfectly, several quantum measurement strategies have been studied for various figures of merits, such as average error probability [1], mutual information [2,3], and success probability of unambiguous state discrimination [4,5,6,7,8,9]. These studies have been motivated not only by academic interest, but also more technological interests from the viewpoints of quantum communication, quantum cryptography, and interferometric sensing.…”

Section: Introductionmentioning

confidence: 99%

Unambiguous quantum-state filtering

2003

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In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum detection probability and its POVM are derived. We applyl such unambiguous quantum state filtering to evaluation of the sensing of decoherence channels. The bounds of the precision limit for a given quantum state of probes and possible device implementations are discussed.

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Optimal Discrimination of Two Nonorthogonal States by Continuous Probing and Feedback Operation

Zhao

2022

Annalen der Physik

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For a quantum system prepared probabilistically on two or more non‐orthogonal states, the observer cannot discriminate the initial preparation perfectly. Kurt Jacobs [Quantum Inf. Comput. 2007, 7, 127] introduced a measurement operator that could increase the rate of information obtained using a continuous measurement scheme. However, the better effect happens at the expense of reducing the total information from the quantum system. To address this problem, an optimal operator that could yield the maximal value of mutual information for a long‐time measurement is found. Particularly, it turns out that the error probability is minimized for any measurement moment by measuring the optimal operator. Furthermore, for a given finite measurement time, a measurement scheme to maximize the obtained mutual information is presented. It is shown that while the Jacobs' operator should be used for a short‐time case, for a long‐time limit, the proposed optimal operator should be employed. For a given finite duration, the proposal could determine the optimal measurement operator that maximizes the final value of mutual information.

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Unambiguous discrimination of mixed states

Cited by 137 publications

References 17 publications

Optimal quantum detectors for unambiguous detection of mixed states

Optimal quantum detectors for unambiguous detection of mixed states

Unambiguous quantum-state filtering

Optimal Discrimination of Two Nonorthogonal States by Continuous Probing and Feedback Operation

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