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Structural approach to unambiguous discrimination of two mixed quantum states

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10.1063/1.3298683

### Abstract

We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 (“solution in four dimensions”). The solution is illustrated by some examples. The optimality conditions proven by Eldar *et al.* [Phys. Rev. A69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy.

© 2010 American Institute of Physics

Received 26 November 2009
Accepted 31 December 2009
Published online 19 March 2010

Acknowledgments: We would like to thank J. Bergou, T. Meyer, Ph. Raynal, Z. Shadman, and R. Unanyan for valuable discussions. This work was partially supported by the EU Integrated Projects SECOQC, SCALA, OLAQUI, QICS and by the FWF.

Article outline:

I. INTRODUCTION

II. DEFINING PROPERTIES OF USD

A. Main definitions

B. Trivial subspaces

C. The role of

III. SIMPLE PROPERTIES OF OPTIMAL MEASUREMENTS

A. Orthogonal subspaces

B. Classification of USD measurements

IV. THE OPTIMALITY CONDITIONS BY ELDAR *et al.*

V. TWO SPECIAL CLASSES OF OPTIMAL MEASUREMENTS

A. Single state detection

B. Fidelity form measurement

VI. SOLUTION IN FOUR DIMENSIONS

A. The measurement class [1,2]

1. The necessary and sufficient conditions

2. Construction of a finite number of candidates for

3. Summary for measurement type (1,2)

B. The measurement class [1,1]

1. Construction of a finite number of candidates for

2. Summary for measurement class [1,1]

C. Examples

VII. GENERAL STRATEGY

VIII. CONCLUSIONS

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2010-03-19

2014-04-25

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