Eur. Phys. J. D (2016) 70: 226
https://doi.org/10.1140/epjd/e2016-70204-8

Regular Article

Minimum error discrimination of equi-coherent bosonic states of n-qubit by separable measurement

¹ Department of Theoretical Physics and Astrophysics, University of Tabriz, 51664 Tabriz, Iran
² Department of Physics, Azarbaijan Shahid Madani University, 53714-161 Tabriz, Iran
³ Marand Faculty of Engineering, University of Tabriz, 5418633184, Tabriz, Iran

^a e-mail: d.akhgar@tabrizu.ac.ir

Received: 19 March 2016
Received in final form: 27 May 2016
Published online: 1 November 2016

Abstract

In this paper, local distinguishability of the multipartite equi-coherent quantum states is studied in the bosonic subspace. A method is proposed to give an upper bound on the optimal success probability in terms of quantum coherence for equiprobable states. Then a necessary and sufficient condition to saturate this upper bound is presented. This condition enables us to give optimal measurements and success probabilities for several examples, including general pure states and n-qubit mixed states which may be linearly dependent. Perfect discrimination is possible for linearly independent states that have maximum quantum coherence. Finally, discrimination of these states when restricted to separable measurements is considered. To this aim an appropriate transformation is proposed to obtain separable measurements equivalent to the optimal measurement, in which the success probability for both is equal. So the upper bound is also valid for separable and LOCC protocol. The important advantage is that for the bosonic measurements it is always possible to obtain equivalent separable operators, not only for minimum error discrimination but also for all strategies of discrimination.