dorsal/arxiv
View SchemaEstimating the spectrum of a density operator
| Authors | M. Keyl, R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102027 |
| URL | https://arxiv.org/abs/quant-ph/0102027 |
| DOI | 10.1103/PhysRevA.64.052311 |
Abstract
Given N quantum systems prepared according to the same density operator \rho, we propose a measurement on the N-fold system which approximately yields the spectrum of \rho. The projections of the proposed observable decompose the Hilbert space according to the irreducible representations of the permutations on N points, and are labeled by Young frames, whose relative row lengths estimate the eigenvalues of \rho in decreasing order. We show convergence of these estimates in the limit N\to\infty, and that the probability for errors decreases exponentially with a rate we compute explicitly.
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"abstract": "Given N quantum systems prepared according to the same density operator \\rho,\nwe propose a measurement on the N-fold system which approximately yields the\nspectrum of \\rho. The projections of the proposed observable decompose the\nHilbert space according to the irreducible representations of the permutations\non N points, and are labeled by Young frames, whose relative row lengths\nestimate the eigenvalues of \\rho in decreasing order. We show convergence of\nthese estimates in the limit N\\to\\infty, and that the probability for errors\ndecreases exponentially with a rate we compute explicitly.",
"arxiv_id": "quant-ph/0102027",
"authors": [
"M. Keyl",
"R. F. Werner"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1103/PhysRevA.64.052311",
"title": "Estimating the spectrum of a density operator",
"url": "https://arxiv.org/abs/quant-ph/0102027"
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