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International Journal of Quantum Information

Unambiguous discrimination between linearly dependent symmetric states with multiple copies

Zhang Shi-jun, Wen‐Hai Zhang

Published Jun 1, 2020• 0 citations
Publisher

Abstract

We investigate the unambiguous discrimination (UD) among three linearly dependent (LD) symmetric states with [Formula: see text] copies. The optimal discrimination probability is derived. Our result shows that a set of linearly dependent symmetric states can be perfectly discriminated as the number of copies goes to infinity.
DOI
10.1142/s021974992050015x

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Given nnn linearly independent pure states and their prior probabilities, we study the optimum unambiguous state discrimination problem. We derive the conditions for the optimum measurement strategy to achieve the maximum average success probability and establish two sets of equations that must be satisfied by the optimum solution in different situations. We also provide the detailed steps to find the optimum measurement strategy. The method and results we obtain are given a geometrical illustration with a numerical example. Furthermore, using these equations, we derive a formula which shows a clear analytical relation between the optimum solution and the nnn states to be discriminated. We also solve a generalized equal-probability measurement problem analytically. Finally, as another application of our result, the unambiguous discrimination problem of three pure states is studied in detail and analytical solutions are obtained for some interesting cases.
The quantum state discrimination problem is ubiquitous in quantum information and serves as the foundation for many quantum communication schemes proposed so far. This paper investigates the optimal discrimination of three symmetric quantum states with equal prior probabilities. To obtain completely accessible information about the input pure states, this strategy makes improvements to the two standard strategies of quantum state discrimination, namely the minimum error discrimination and unambiguous discrimination. The new discrimination strategy proposed in this paper can be applied to both linearly independent and dependent quantum states.
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