1. Linear preservers and quantum information science.
- Author
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Fošner, Ajda, Huang, Zejun, Li, Chi-Kwong, and Sze, Nung-Sing
- Subjects
- *
LINEAR statistical models , *QUANTUM information science , *OPERATOR theory , *HERMITIAN operators , *MATRICES (Mathematics) , *TENSOR algebra , *IDENTITIES (Mathematics) - 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]
- Published
- 2013
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