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Conclusive Discrimination by N Sequential Receivers between r≥2 Arbitrary Quantum States
In the present article, we develop a general mathematical framework for discrimination between r ≥ 2 quantum states by N ≥ 1 sequential receivers in the case where each re- ceiver obtains a conclusive result. This type of discrimination constitutes an N-sequential extension of the minimum-error discrimination by one receiver. The developed general framework, which is valid for a conclusive discrimination between any number r ≥ 2 of quantum states, pure or mixed, of an arbitrary dimension and any number N ≥ 1 of se- quential receivers, is based on the notion of a quantum state instrument, and this allows us to derive the new important general results. We, in
particular, find a general condition on r ≥ 2 quantum states, under which, within the strategy
where all types of receivers’ quantum measurements are allowed, the optimal success probability of the N-sequential conclusive discrimination between these r ≥ 2 states is equal to that of the first receiver for any number N ≥ 2 of further sequential receivers and specify the corresponding optimal protocol. Furthermore, we extend our general framework to include an N- sequential conclusive discrimination between r ≥ 2 arbitrary quantum states under a noisy commu- nication. As an example, we analyze analytically and numerically a two-sequential con- clusive discrimination between two qubit states via depolarizing quantum channels. The derived new general results are important both from the theoretical point of view and for the development of a successful multipartite quantum
communication via noisy quantum channels.