Generalization of quantum-state comparison

We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities....

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2005-09, Vol.72 (3), Article 032308
Main Authors: Kleinmann, M., Kampermann, H., Bruß, D.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
COMPARATIVE EVALUATIONS
ENERGY LEVELS
MATHEMATICAL SOLUTIONS
MIXED STATE
PROBABILITY
QUANTUM MECHANICS
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Summary:We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities. We show that the optimal coherent measurement is always superior to the optimal incoherent measurement. Second, we develop a strategy for the comparison of two states from a set of N pure states, and find an optimal solution for some parameter range when N=3. In both cases we use the reduction method for the corresponding problem of mixed-state discrimination, as introduced by Raynal et al., which reduces the problem to the discrimination of two pure states only for N=2. Finally, we provide a necessary and sufficient condition for unambiguous comparison of mixed states to be possible.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.72.032308