Relation between minimum-error discrimination and optimum unambiguous discrimination
- Department of Computer Science, Sun Yat-sen University, Guangzhou 510006 (China)
In this paper, we investigate the relationship between the minimum-error probability Q{sub E} of ambiguous discrimination and the optimal inconclusive probability Q{sub U} of unambiguous discrimination. It is known that for discriminating two states, the inequality Q{sub U{>=}}2Q{sub E} has been proved in the literature. The main technical results are as follows: (1) We show that, for discriminating more than two states, Q{sub U{>=}}2Q{sub E} may not hold again, but the infimum of Q{sub U}/Q{sub E} is 1, and there is no supremum of Q{sub U}/Q{sub E}, which implies that the failure probabilities of the two schemes for discriminating some states may be narrowly or widely gapped. (2) We derive two concrete formulas of the minimum-error probability Q{sub E} and the optimal inconclusive probability Q{sub U}, respectively, for ambiguous discrimination and unambiguous discrimination among arbitrary m simultaneously diagonalizable mixed quantum states with given prior probabilities. In addition, we show that Q{sub E} and Q{sub U} satisfy the relationship that Q{sub U{>=}}(m/m-1)Q{sub E}.
- OSTI ID:
- 21448671
- Journal Information:
- Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.032333; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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