Exact Eigenanalyses of Certain N^m x N^m Density Matrices
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.
Keywords
Cite
@article{arxiv.quant-ph/9806039,
title = {Exact Eigenanalyses of Certain N^m x N^m Density Matrices},
author = {Paul B. Slater},
journal= {arXiv preprint arXiv:quant-ph/9806039},
year = {2007}
}
Comments
We are withdrawing this paper because we have now been able to conduct analyses for the case N=3, m =3 and wish to incorporate these further results. Accordingly, a new paper will shortly be issued, tentatively entitled, "SU(N) x S_{m}-Invariant Eigenspaces of N^{m} x N^{m} Mean Density Matrices"