On quantum detection and the square-root measurement
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Publication:4544526
DOI10.1109/18.915636zbMATH Open1020.94509arXivquant-ph/0005132OpenAlexW2106770754MaRDI QIDQ4544526
Author name not available (Why is that?)
Publication date: 4 August 2002
Published in: (Search for Journal in Brave)
Abstract: In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal 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 [Phys. Rev. Lett. 66, 1119 (1991)] and Hausladen et al. [Phys. Rev. A 54, 1869 (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. [Int. J. Theor. Phys. 36, 1269 (1997)].
Full work available at URL: https://arxiv.org/abs/quant-ph/0005132
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