Generating random density matrices

被引:133
作者
Zyczkowski, Karol [1 ,2 ]
Penson, Karol A. [3 ]
Nechita, Ion [4 ,5 ]
Collins, Benoit [4 ,6 ]
机构
[1] Jagiellonian Univ, Inst Phys, Ul Reymonta 4, PL-30059 Krakow, Poland
[2] Polish Acad Sci, Ctr Fizyki Teoretycznej, PL-02668 Warsaw, Poland
[3] Univ Paris 06, Lab Phys Mat Condensee LPTMC, CNRS, UMR 7600, F-75252 Paris 05, France
[4] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada
[5] Univ Toulouse, Phys Theor Lab, CNRS, IRSAMC,UPS, F-31062 Toulouse, France
[6] Univ Lyon 1, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France
基金
加拿大自然科学与工程研究理事会;
关键词
MIXED QUANTUM STATES; ENSEMBLES; UNITARY; ENTROPY; VOLUME; SET;
D O I
10.1063/1.3595693
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi-partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N -> infinity, by the Marchenko-Pastur distribution. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3595693]
引用
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页数:20
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