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Linear preservers and quantum information science.
- Source :
-
Linear & Multilinear Algebra . Oct2013, Vol. 61 Issue 10, p1377-1390. 14p. - Publication Year :
- 2013
-
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 onmn × mnHermitian matrices such that φ(A ⊗ B) andA ⊗ Bhave the same spectrum for anym × mHermitianAandn × nHermitianB. Such a map has the formA ⊗ B ↦ U(ϕ1(A) ⊗ ϕ2(B))U* formn × mnHermitian matrices in tensor formA ⊗ B, whereUis a unitary matrix, and forj ∈ {1, 2}, ϕjis the identity map X ↦ Xor the transposition map X ↦ Xt. The structure of linear maps leaving invariant the spectral radius of matrices in tensor formA ⊗ Bis also obtained. The results are connected to bipartite (quantum) systems and are extended to multipartite systems. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 61
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 90364125
- Full Text :
- https://doi.org/10.1080/03081087.2012.740029