dorsal/arxiv
View SchemaQuantum Detection with Unknown States
| Authors | Noam Elron, Yonina C. Eldar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501084 |
| URL | https://arxiv.org/abs/quant-ph/0501084 |
| DOI | 10.1103/PhysRevA.72.032338 |
Abstract
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the probability of a detection error have been derived. In this work, we assume that each of the states in our collection is a mixture of a known state and an unknown state. We investigate two criteria for optimality. The first is minimization of the worst-case probability of a detection error. For the second we assume a probability distribution on the unknown states, and minimize of the expected probability of a detection error. We find that under both criteria, the optimal detectors are equivalent to the optimal detectors of an ``effective ensemble''. In the worst-case, the effective ensemble is comprised of the known states with altered prior probabilities, and in the average case it is made up of altered states with the original prior probabilities.
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"abstract": "We address the problem of distinguishing among a finite collection of quantum\nstates, when the states are not entirely known. For completely specified\nstates, necessary and sufficient conditions on a quantum measurement minimizing\nthe probability of a detection error have been derived. In this work, we assume\nthat each of the states in our collection is a mixture of a known state and an\nunknown state. We investigate two criteria for optimality. The first is\nminimization of the worst-case probability of a detection error. For the second\nwe assume a probability distribution on the unknown states, and minimize of the\nexpected probability of a detection error.\n We find that under both criteria, the optimal detectors are equivalent to the\noptimal detectors of an ``effective ensemble\u0027\u0027. In the worst-case, the\neffective ensemble is comprised of the known states with altered prior\nprobabilities, and in the average case it is made up of altered states with the\noriginal prior probabilities.",
"arxiv_id": "quant-ph/0501084",
"authors": [
"Noam Elron",
"Yonina C. Eldar"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.032338",
"title": "Quantum Detection with Unknown States",
"url": "https://arxiv.org/abs/quant-ph/0501084"
},
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