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

Herzog, Ulrike

doi:10.1103/physreva.86.032314

Cited by 42 publications

(48 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the other region, we get M opt 0 = 0, M opt 1 = 0, and M opt 2 = 0, which coincides with the previous result [35].…”

Section: (45)supporting

confidence: 91%

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

Kwon

2017

Quantum Inf Process

View full text Add to dashboard Cite

In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results. Our strategy is to transform the problem of two qubit states into a minimum error discrimination for three qubit states by adding a specific quantum state ρ0 and a prior probability q0, which behaves as an inconclusive degree. First, we introduce the beginning and the end of practical interval of inconclusive result, q (0) 0 and q (1) 0 , which are key ingredients in investigating our problem. Then we obtain the analytic form of them. Next, we show that our problem can be classified into two cases q0 = q 0 . In fact, by maximum confidences of two qubit states and non-diagonal element of ρ0, the our problem is completely understood. We provide an analytic solution of our problem when q0 = q (1) 0 , we rather supply the numerical method to find the solution, because of the complex relation between inconclusive degree and corresponding failure probability. Finally we confirm our results using previously known examples.

show abstract

“…In the other region, we get M opt 0 = 0, M opt 1 = 0, and M opt 2 = 0, which coincides with the previous result [35].…”

Section: (45)supporting

confidence: 91%

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

Kwon

2017

Quantum Inf Process

View full text Add to dashboard Cite

show abstract

“…Recently we became aware of two recent related works [34,35]. In both works, discrimination with a fixed rate of inconclusive results is applied to the set of symmetric states and it is argued that the results can be transformed to solutions for discrimination with the error margin.…”

Section: Discussionmentioning

confidence: 99%

Discrimination with an error margin among three symmetric states of a qubit

2012

View full text Add to dashboard Cite

We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three symmetric pure states of a qubit. The measurements are classified into three types, and one of the three types is optimal depending on the value of the error margin. The problem is formulated as one of semidefinite programming. Starting with the dual problem derived from the primal one, we analytically obtain the optimal success probability and the optimal measurement that attains it in each domain of the error margin. Moreover, we analyze the case of three symmetric mixed states of a qubit.

show abstract

“…Note that an optimal error margin measurement has strong relationship with an optimal inconclusive measurement [24,25]. However, if one wants to obtain an optimal error margin measurement for a given ε, then one needs to solve problem (7) instead of the problem of finding an optimal inconclusive measurement.…”

Section: Optimal Error Margin Measurementmentioning

confidence: 99%

Generalized quantum state discrimination problems

2015

View full text Add to dashboard Cite

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

show abstract

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

Cited by 42 publications

References 42 publications

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

Discrimination with an error margin among three symmetric states of a qubit

Generalized quantum state discrimination problems

Contact Info

Product

Resources

About