Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
- Institut fuer Physik, Humboldt-Universitaet zu Berlin, Newtonstrasse 15, D-12489 Berlin (Germany)
- Department of Physics and Astronomy, Hunter College, City University of New York, 695 Park Avenue, New York, New York 10021 (United States)
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is ambiguous discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i.e., error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum-error probability achievable in ambiguous discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case where the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison with the minimum failure probability.
- OSTI ID:
- 20645847
- Journal Information:
- Physical Review. A, Vol. 70, Issue 2; Other Information: DOI: 10.1103/PhysRevA.70.022302; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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