On quantum detection and the square-root measurement

We consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure (POVM) consisting of rank-one operators with measurement vectors closest in...

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Bibliographic Details
Published in:IEEE transactions on information theory 2001-03, Vol.47 (3), p.858-872
Main Authors: Eldar, Y.C., Forney, G.D.
Format: Article
Language:English
Subjects:
Collection
Error detection
Information technology
INT
Least squares method
Mathematical analysis
Norms
Optical signal detection
Optimization
Quantum theory
Vectors (mathematics)
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Summary:We consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure (POVM) consisting of rank-one operators with measurement vectors closest in squared norm to the given states. We compare our results to previous measurements suggested by Peres and Wootters (1991) and Hausladen et al. (1996), where we refer to the latter as the square-root measurement (SRM). We obtain a new characterization of the SRM, and prove that it is optimal in a least-squares sense. In addition, we show that for a geometrically uniform state set the SRM minimizes the probability of a detection error. This generalizes a similar result of Ban et al. (see Int. J. Theor. Phys., vol.36, p.1269-88, 1997).
ISSN:0018-9448
1557-9654
DOI:10.1109/18.915636