Linear preservers and quantum information science |
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| Authors: | Ajda Fo?ner Zejun Huang Chi-Kwong Li |
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| Institution: | 1. Faculty of Management , University of Primorska , Cankarjeva 5, SI-6104 Koper , Slovenia;2. Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Hong Kong;3. Department of Mathematics , College of William and Mary , Williamsburg , VA 23187 , USA;4. Department of Mathematics , University of Hong Kong , Pokfulam , Hong Kong |
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| 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???U(?1(A)????2(B))U* for mn?×?mn Hermitian matrices in tensor form A???B, where U is a unitary matrix, and for j?∈?{1,?2}, ? j is the identity map?X???X or the transposition map?X???X t . 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. |
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| Keywords: | Hermitian matrix linear preserver spectrum spectral radius tensor state |
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