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Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - Nanooptik

Humboldt-Universität zu Berlin | Mathematisch-Naturwissen­schaft­liche Fakultät | Institut für Physik | Nanooptik | Publications | Minimum-error strategy for discriminating between subsets of nonorthogonal quantum states

Ulrike Herzog and János A Bergou (2003)

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

Fortschritte der Physik, 51(2-3):140-144.

We 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.