dorsal/arxiv
View SchemaQuantum state estimation and large deviations
| Authors | M. Keyl |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412053 |
| URL | https://arxiv.org/abs/quant-ph/0412053 |
| DOI | 10.1142/S0129055X06002565 |
| Journal | Reviews in Mathematical Physics, Vol. 18, No. 1 (2006) 19-60 |
Abstract
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.
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"abstract": "In this paper we propose a method to estimate the density matrix \\rho of a\nd-level quantum system by measurements on the N-fold system. The scheme is\nbased on covariant observables and representation theory of unitary groups and\nit extends previous results concerning the estimation of the spectrum of \\rho.\nWe show that it is consistent (i.e. the original input state \\rho is recovered\nwith certainty if N \\to \\infty), analyze its large deviation behavior, and\ncalculate explicitly the corresponding rate function which describes the\nexponential decrease of error probabilities in the limit N \\to \\infty. Finally\nwe discuss the question whether the proposed scheme provides the fastest\npossible decay of error probabilities.",
"arxiv_id": "quant-ph/0412053",
"authors": [
"M. Keyl"
],
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"quant-ph",
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],
"doi": "10.1142/S0129055X06002565",
"journal_ref": "Reviews in Mathematical Physics, Vol. 18, No. 1 (2006) 19-60",
"title": "Quantum state estimation and large deviations",
"url": "https://arxiv.org/abs/quant-ph/0412053"
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