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Journal of Modern Optics

Unambiguous discrimination among three linearly independent symmetric states

Wen‐Hai Zhang, Wenyan Nie, Gang Ren

Published Apr 22, 2019• 0 citations
Publisher

Abstract

We investigate the unambiguous discrimination of three linearly independent symmetric states. We derive the minimum inconclusive probability by using an ancillary system and introducing a unitary transformation which acts on the input states and produces the output measured on the ancilla. We generalize to the case of discriminating the symmetric states with multiple copies. Our results show that the minimum inconclusive probabilities can be expressed as a form, not only dependent on the modular and the phase factors but also dependent on the number of the copies.

DOI
10.1080/09500340.2019.1606951

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In this paper, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. With a constructive procedure, we establish a necessary and sufficient condition for feasible POVM measurements for unambiguous quantum state discrimination. We develop methods to calculate the optimal discrimination efficiencies for minimizing the inconclusive probability and the optimal discrimination efficiencies for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a feasible POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform states with equal a priori probabilities meet this condition.