Minimum error discrimination between similarity-transformed quantum states
- Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz 51664 (Iran, Islamic Republic of)
Using the well-known necessary and sufficient conditions for minimum error discrimination (MED), we extract an equivalent form for the MED conditions. In fact, by replacing the inequalities corresponding to the MED conditions with an equivalent but more suitable and convenient identity, the problem of mixed state discrimination with optimal success probability is solved. Moreover, we show that the mentioned optimality conditions can be viewed as a Helstrom family of ensembles under some circumstances. Using the given identity, MED between N similarity transformed equiprobable quantum states is investigated. In the case that the unitary operators are generating a set of irreducible representation, the optimal set of measurements and corresponding maximum success probability of discrimination can be determined precisely. In particular, it is shown that for equiprobable pure states, the optimal measurement strategy is the square-root measurement (SRM), whereas for the mixed states, SRM is not optimal. In the case that the unitary operators are reducible, there is no closed-form formula in the general case, but the procedure can be applied in each case in accordance to that case. Finally, we give the maximum success probability of optimal discrimination for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, spin-j states, particular nonsymmetric qudit states, etc.
- OSTI ID:
- 22038585
- Journal Information:
- Physical Review. A, Vol. 84, Issue 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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