Minimum‐error strategy for discriminating between subsets of nonorthogonal quantum states

Abstract

AbstractWe consider a quantum system that is prepared, with a given a priori probability, in a pure state that belongs to a known set of N nonorthogonal quantum states. We study a minimum‐error measurement for assigning the state of the system to one or the other of two complementary subsets of the set of the given states. For the case that the N states span a Hilbert space that is only two‐dimensional, a simple analytical solution is derived for the minimum error probability and the optimum measurement strategy. If one of the subsets contains only a single state, the measurement is referred to as quantum state filtering. Our general result is applied to investigate minimum‐error quantum state filtering of three arbitrary linearly dependent states. Moreover, we discuss a generalized measurement for performing minimum‐error filtering of three special linearly independent states.