On Quantum Detection and the Square-Root Measurement
| dc.creator | Eldar, Yonina C. | |
| dc.creator | Forney Jr, G. David | |
| dc.date | 2000-05-31 | |
| dc.date | 2000-08-29 | |
| dc.date.accessioned | 2026-07-07T06:00:06Z | |
| dc.date.available | 2026-07-07T06:00:06Z | |
| dc.description | 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)]. | |
| dc.description | Version of August 29, 2000, with minor revisions. To appear in the IEEE Transactions on Information Theory. RevTex, 48 pages, 3 figures. A briefer version of this paper has also been submitted to Physical Review Letters. A copy is obtainable by writing to the authors at yonina@mit.edu | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0005132 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0005132 | |
| dc.identifier | IEEE Trans. Inform. Theory, vol. 47, pp. 858-872, Mar. 2001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88904 | |
| dc.subject | Quantum Physics | |
| dc.title | On Quantum Detection and the Square-Root Measurement | |
| dc.type | text |