DocumentCode :
1464777
Title :
On quantum detection and the square-root measurement
Author :
Eldar, Yonina C. ; Forney, G. David, Jr.
Author_Institution :
Res. Lab. of Electron., MIT, Cambridge, MA, USA
Volume :
47
Issue :
3
fYear :
2001
fDate :
3/1/2001 12:00:00 AM
Firstpage :
858
Lastpage :
872
Abstract :
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)
Keywords :
error statistics; least squares approximations; measurement theory; optical signal detection; detection error probability; geometrically uniform state; measurement vectors; nonorthogonal quantum states; optimal least-squares; positive operator-valued measure; pure states; quantum detection; rank-one operators; square-root measurement; Collaborative work; Costs; Information theory; Instruments; Laboratories; Performance evaluation; Quantum mechanics; Singular value decomposition; Sufficient conditions; Transmitters;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.915636
Filename :
915636
Link To Document :
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