Minimum-error discrimination between symmetric mixed quantum states

Chou, Chia-Fu; Hsu, Li-Yi

doi:10.1103/physreva.68.042305

Cited by 80 publications

(64 citation statements)

References 12 publications

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“…It is a difficult problem for giving an analytical solution for ambiguously distinguishing between any m given mixed states, and only some special cases has been solved [11,12,13,14,15].…”

Section: Discussionmentioning

confidence: 99%

“…For the case of more than two quantum states, necessary and sufficient conditions have been derived for an optimum measurement maximizing the success probability of correct detection [5,6,8]. However, analytical solutions for an optimum measurement have been obtained only for some special cases [11,12,13,14,15], and, as pointed out in [8], obtaining a concrete expression for an optimum measurement in the general case is a difficult and unsolved problem.…”

Section: Introductionmentioning

confidence: 99%

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Minimum-error discrimination between mixed quantum states

Qiu

2008

Phys. Rev. A

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We derive a general lower bound on the minimum-error probability for ambiguous discrimination between arbitrary m mixed quantum states with given prior probabilities. When m = 2, this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out a upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimumerror probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimumerror probability for ambiguously discriminating arbitrary m mixed quantum states with the optimal failure probability for unambiguously discriminating the same states.

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“…It is a difficult problem for giving an analytical solution for ambiguously distinguishing between any m given mixed states, and only some special cases has been solved [11,12,13,14,15].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum-error discrimination between mixed quantum states

Qiu

2008

Phys. Rev. A

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“…(This approach will be justified in the next section, where we design an optical scheme that implements the MC measurement.) Therefore, we look for a unitary operation acting on the entire space that will couple those extra dimensions to the original system and, finally, a projective measurement on this space to accomplish the POVM (27). To start with, let us consider a set of orthonormal extended states {|υ j }, defined as…”

Section: B Successmentioning

confidence: 99%

“…For this so-called minimum error strategy (ME), the necessary and sufficient conditions that must be satisfied by the operators describing the optimized measurement are well known [12,13]. Nevertheless, only for a few special cases the explicit form of such measurements have been found [11,13,[26][27][28][29]. A second strategy, first proposed by Ivanovic [30], allows one to identify each state in the set without error but with the possibility of obtaining an inconclusive result.…”

Section: Introductionmentioning

confidence: 99%

Maximum-confidence discrimination among symmetric qudit states

et al. 2011

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We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of "sequential maximum-confidence" (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.Comment: 14 pages, 4 figures. Published versio

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“…These two forms of discrimination are the extreme cases of procedures for which errors and inconclusive outcomes are both possible [12]. Conclusive discrimination and unambiguous discrimination have been extended in many directions: to more than two possible pure states [13,14], to sets of states (quantum state filtering) [15,16], and to mixed states [17,18]. By weak discrimination we mean discrimination among two or more quantum states based on one or more weak measurements.…”

Section: Weak Discriminationmentioning

confidence: 98%

<title>A Gaussian quantum state discriminator</title>

Frey

Szymonifka

2005

SPIE Proceedings

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A Gaussian statistic, or discriminator, is proposed for conclusively discriminating between two pure quantum states. The discriminator is based on registrations from a limit of an increasing number of weak measurements on a single system. The average error of the discriminator is near that of the optimal conclusive Helstrom discriminator and, in fact, the Gaussian discriminator is the limit point of a class of conclusive discriminators which includes the Helstrom discriminator. The Gaussian discriminator always leaves some post-measurement state (PMS) separation; by contrast, the PMS separation with the Helstrom discriminator is always zero. Simple, closed-form expressions are given for the distribution and error performance of the Gaussian discriminator.

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Minimum-error discrimination between symmetric mixed quantum states

Cited by 80 publications

References 12 publications

Minimum-error discrimination between mixed quantum states

Minimum-error discrimination between mixed quantum states

Maximum-confidence discrimination among symmetric qudit states

<title>A Gaussian quantum state discriminator</title>

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