Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/18377
Title: Linear preservers and quantum information science
Authors: Fosner, A
Huang, Z
Li, CK
Sze, NS 
Keywords: Hermitian matrix
Linear preserver
Spectral radius
Spectrum
Tensor state
Issue Date: 2013
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2013, v. 61, no. 10, p. 1377-1390 How to cite?
Journal: Linear and multilinear algebra 
Abstract: In this article, a brief survey of recent results on linear preserver problems and quantum information science is given. In addition, characterization is obtained for linear operators φ on mn × mn Hermitian matrices such that φ(A ⊗ B) and A ⊗ B have the same spectrum for any m × m Hermitian A and n × n Hermitian B. Such a map has the form A ⊗ B {mapping} U(φ1(A) ⊗ φ2(B))U* for mn × mn Hermitian matrices in tensor form A ⊗ B, where U is a unitary matrix, and for j ∈ {1,2}, φj is the identity map X {mapping} X or the transposition map X {mapping} Xt. The structure of linear maps leaving invariant the spectral radius of matrices in tensor form A ⊗ B is also obtained. The results are connected to bipartite (quantum) systems and are extended to multipartite systems.
URI: http://hdl.handle.net/10397/18377
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2012.740029
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