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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 PublicationJournal of Physics A: Mathematical and Theoretical
ISSN17518121 17518113
Volume43Issue: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.

DOI10.1088/1751-8113/43/31/315303
URLView the original
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000279874800016
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Cited Times [WOS]:16   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorChen Y.
Affiliation1.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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