一类N^m × N^m密度矩阵的精确特征分析
Exact Eigenanalyses of Certain N^m x N^m Density Matrices
摘要：
我们应用和扩展最近的结果Krattenthaler和斯莱特（quant-ph/9612043），谁寻求量子类似物的开创性工作的通用数据压缩的克拉克和巴伦。KS对2 × 2密度矩阵的m重张量积求平均，得到了2 × 2密度矩阵的特征值和特征向量的显式表达式.加权是相对于一个单参数的概率分布族进行的，该概率分布族的所有成员在二能级量子系统的“布洛赫球”上是球对称的。该族包括最小单调（Bures）度量的归一化体积元素。在这封信中，我们进行平行分析（为m = 2，3，4），根据自然措施的密度矩阵最近提出的Zyczkowski，Horodecki，Sanpera和Lewenstein（quant-ph/9804024），并发现有趣的相似性和差异的发现KS。此外，我们还得到了3 × 3密度矩阵的二重张量积在ZHSL测度下的类似结果。
英文摘要：
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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