Optimum testing of multiple hypotheses in quantum detection theory

Yuen, Horace P.; Kennedy, Robert S.; Lax, M.

doi:10.1109/tit.1975.1055351

Cited by 458 publications

(488 citation statements)

References 15 publications

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“…This problem may be roughly described in this manner [1,2,3,4,5,6]: Suppose that a transmitter, Alice, wants to convey classical information to a receiver, Bob, using a quantum channel, and Alice represents the message conveyed as a mixed quantum state that, with given prior probabilities, belongs to a finite set of mixed quantum states, say {ρ 1 , ρ 2 , . .…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Minimum-error discrimination between mixed quantum states

Qiu

2008

Phys. Rev. A

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“…The first papers dealing with quantum statistical problems appeared in the seventies [23,56,55,6,24] and tackled issues such as quantum Cramér-Rao bounds for unbiased estimators, optimal estimation for families of states possessing a group symmetry, estimation of Gaussian states, optimal discrimination between non-commuting states. In recent years there has been a renewed interest in the field [21,22,36,5] and the advances in quantum engineering have led to the first practical implementations of theoretical methods [1,16,43].…”

Section: Introductionmentioning

confidence: 99%

Local Asymptotic Normality in Quantum Statistics

Guţǎ

Jenčová

2007

Commun. Math. Phys.

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The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family ϕ n θ 0 +u/ √ n consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state φu of an algebra of canonical commutation relations. The convergence holds for all "local parameters" u ∈ R m such that θ = θ0 + u/ √ n parametrizes a neighborhood of a fixed point θ0 ∈ Θ ⊂ R m . In order to prove the result we define weak and strong convergence of quantum statistical experiments which extend to the asymptotic framework the notion of quantum sufficiency introduces by Petz. Along the way we introduce the concept of canonical state of a statistical experiment, and investigate the relation between the two notions of convergence. For reader's convenience and completeness we review the relevant results of the classical as well as the quantum theory.

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“…Several approaches have emerged to distinguishing between a collection of nonorthogonal quantum states. In one approach, a measurement is designed to minimize the probability of a detection error [1][2][3][4][5][6][7][8][9][10]. A more recent approach, referred to as unambiguous detection [11][12][13][14][15][16][17][18][19], is to design a measurement that with a certain probability returns an inconclusive result, but such that if the measurement returns an answer, then the answer is correct with probability 1.…”

Section: Introductionmentioning

confidence: 99%

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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Optimum testing of multiple hypotheses in quantum detection theory

Cited by 458 publications

References 15 publications

Minimum-error discrimination between mixed quantum states

Minimum-error discrimination between mixed quantum states

Local Asymptotic Normality in Quantum Statistics

Optimal quantum detectors for unambiguous detection of mixed states

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