dorsal/arxiv
View SchemaOn Quantum Detection and the Square-Root Measurement
| Authors | Yonina C. Eldar, G. David Forney Jr |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005132 |
| URL | https://arxiv.org/abs/quant-ph/0005132 |
| Journal | IEEE Trans. Inform. Theory, vol. 47, pp. 858-872, Mar. 2001 |
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)].
{
"annotation_id": "276c9e06-53d6-4ef3-abe7-354a92ad3861",
"date_created": "2026-03-02T18:01:38.731000Z",
"date_modified": "2026-03-02T18:01:38.731000Z",
"file_hash": "3bf884a2c320ddf659292bd9927f0fb50b7e369ea7ecdd4c8b585d63927ccc0c",
"private": false,
"record": {
"abstract": "In this paper we consider the problem of constructing measurements optimized\nto distinguish between a collection of possibly non-orthogonal quantum states.\nWe consider a collection of pure states and seek a positive operator-valued\nmeasure (POVM) consisting of rank-one operators with measurement vectors\nclosest in squared norm to the given states. We compare our results to previous\nmeasurements suggested by Peres and Wootters [Phys. Rev. Lett. 66, 1119 (1991)]\nand Hausladen et al. [Phys. Rev. A 54, 1869 (1996)], where we refer to the\nlatter as the square-root measurement (SRM). We obtain a new characterization\nof the SRM, and prove that it is optimal in a least-squares sense. In addition,\nwe show that for a geometrically uniform state set the SRM minimizes the\nprobability of a detection error. This generalizes a similar result of Ban et\nal. [Int. J. Theor. Phys. 36, 1269 (1997)].",
"arxiv_id": "quant-ph/0005132",
"authors": [
"Yonina C. Eldar",
"G. David Forney Jr"
],
"categories": [
"quant-ph"
],
"journal_ref": "IEEE Trans. Inform. Theory, vol. 47, pp. 858-872, Mar. 2001",
"title": "On Quantum Detection and the Square-Root Measurement",
"url": "https://arxiv.org/abs/quant-ph/0005132"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d719c755-c4f1-4860-a2e8-35faa5ace2a0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}