dorsal/arxiv
View SchemaExact Eigenanalyses of Certain N^m x N^m Density Matrices
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806039 |
| URL | https://arxiv.org/abs/quant-ph/9806039 |
Abstract
We apply and extend recent results of Krattenthaler and Slater (quant-ph/9612043), who sought quantum analogs of seminal work on universal data compression of Clarke and Barron. KS obtained explicit formulas for the eigenvalues and eigenvectors of the 2^m x 2^m density matrices gotten by averaging the m-fold tensor products with themselves of the 2 x 2 density matrices. The weighting was done with respect to a one-parameter family of probability distributions, all the members of which are spherically-symmetric over the "Bloch sphere" of two-level quantum systems. This family includes the normalized volume element of the minimal monotone (Bures) metric. In this letter, we conduct parallel analyses (for m =2,3,4), based on a natural measure on the density matrices recently proposed by Zyczkowski, Horodecki, Sanpera and Lewenstein (quant-ph/9804024) and find interesting similarities and differences with the findings of KS. In addition, we are able to obtain exact analogous results, based on the measure of ZHSL, for the twofold tensor products of the 3 x 3 density matrices.
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"abstract": "We apply and extend recent results of Krattenthaler and Slater\n(quant-ph/9612043), who sought quantum analogs of seminal work on universal\ndata compression of Clarke and Barron. KS obtained explicit formulas for the\neigenvalues and eigenvectors of the 2^m x 2^m density matrices gotten by\naveraging the m-fold tensor products with themselves of the 2 x 2 density\nmatrices. The weighting was done with respect to a one-parameter family of\nprobability distributions, all the members of which are spherically-symmetric\nover the \"Bloch sphere\" of two-level quantum systems. This family includes the\nnormalized volume element of the minimal monotone (Bures) metric. In this\nletter, we conduct parallel analyses (for m =2,3,4), based on a natural measure\non the density matrices recently proposed by Zyczkowski, Horodecki, Sanpera and\nLewenstein (quant-ph/9804024) and find interesting similarities and differences\nwith the findings of KS. In addition, we are able to obtain exact analogous\nresults, based on the measure of ZHSL, for the twofold tensor products of the 3\nx 3 density matrices.",
"arxiv_id": "quant-ph/9806039",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"title": "Exact Eigenanalyses of Certain N^m x N^m Density Matrices",
"url": "https://arxiv.org/abs/quant-ph/9806039"
},
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