Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble | |
Chen Y.1; Liu D.-Z.2; Zhou D.-S.3 | |
2010-07-06 | |
Source Publication | Journal of Physics A: Mathematical and Theoretical |
ISSN | 17518121 17518113 |
Volume | 43Issue:31 |
Abstract | In this paper we study the entanglement of the reduced density matrix of a bipartite quantum system in a random pure state. It transpires that this involves the computation of the smallest eigenvalue distribution of the fixed-trace Laguerre ensemble of N × N random matrices. We showed that for finite N the smallest eigenvalue distribution may be expressed in terms of Jack polynomials. Furthermore, based on the exact results, we found a limiting distribution when the smallest eigenvalue is suitably scaled with N followed by a large N limit. Our results turn out to be the same as the smallest eigenvalue distribution of the classical Laguerre ensembles without the fixed-trace constraint. This suggests in a broad sense, the global constraint does not influence local correlations, at least, in the large N limit. Consequently, we have solved an open problem: the determination of the smallest eigenvalue distribution of the reduced density matrix-obtained by tracing out the environmental degrees of freedom-for a bipartite quantum system of unequal dimensions. |
DOI | 10.1088/1751-8113/43/31/315303 |
URL | View the original |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Physics |
WOS Subject | Physics, Multidisciplinary ; Physics, Mathematical |
WOS ID | WOS:000279874800016 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Chen Y. |
Affiliation | 1.Department of Mathematics, Imperial College London, 180 Queens Gates, London SW7 2BZ, UK 2.School of Mathematical Sciences, Peking University, Beijing, 100871, People's Republic of China 3.Department of Mathematics, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, People's Republic of China |
Recommended Citation GB/T 7714 | Chen Y.,Liu D.-Z.,Zhou D.-S.. Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble[J]. Journal of Physics A: Mathematical and Theoretical,2010,43(31). |
APA | Chen Y.,Liu D.-Z.,&Zhou D.-S..(2010).Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble.Journal of Physics A: Mathematical and Theoretical,43(31). |
MLA | Chen Y.,et al."Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble".Journal of Physics A: Mathematical and Theoretical 43.31(2010). |
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