Linear preservers and quantum information science

Ajda Fošner, Zejun Huang, Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)

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}, φjis 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.
Original languageEnglish
Pages (from-to)1377-1390
Number of pages14
JournalLinear and Multilinear Algebra
Volume61
Issue number10
DOIs
Publication statusPublished - 16 Dec 2013

Keywords

  • Hermitian matrix
  • Linear preserver
  • Spectral radius
  • Spectrum
  • Tensor state

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this