Minimum-error discrimination between a pure and a mixed two-qubit state.pdf

arXiv:quant-ph/0307038v1 5 Jul 2003 Minimum-error discrimination between a pure and a mixed two-qubit state Ulrike Herzog Institut f¨ur Physik, Humboldt-Universit¨at Berlin, Newtonstrasse 15, D-12489 Berlin, Germany The problem of discriminating with minimum error between two mixed quantum states is re- viewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability oferrors in deciding whether the state of a quantum system is either a given pure state or a uniform statistical mixture of any number of mutually orthogonal states. The result is applied to two-qubit states, and the minimum error probabilities achievable by collective and local measurements on the qubits pared. PACS numbers: -a, , .-p I. INTRODUCTION Quantum state discrimination [1] is of fundamental importance for munication and quantum cryp- tography. The problem consists in determining the state of asingle copy of a quantum system that is prepared in a certain but unknown state, belonging to a given ?nite set of known states which occur with given a-priori probabilities. When the quantumstates are non-orthogonal, it is impossible to device a measurement that can discriminate between them perfectly. Therefore strategies for an optimal measurement have been developed with respect to various criteria. Unambig