Linear maps preserving determinant of tensor products of Hermitian matrices

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• 作者：Yuting Ding^a ; ^{yuting840810@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ajda Fo&scaron ; ner^b ; ^{ajda.fosner@fm-kp.si" class="auth_mail" title="E-mail the corresponding author} ; Jinli Xu^a ; ^{jclixv@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Baodong Zheng^c ; ^{zbd@hit.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Linear preserver ; Tensor product ; Determinant ; Hermitian matrix ; Quantum information science
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1139-1153
• 全文大小：359 K

文摘

Let m,n≥2$m,n\ge 2$ be positive integers and let H_n$H_n$ be the set of 11dc687009b172d410fb7678924c7ff" title="Click to view the MathML source">n×n$n\times n$ complex Hermitian matrices. We study linear maps ϕ:H_mn→H_mn$\varphi :H_{mn}\to H_{mn}$ satisfying det⁡(A⊗B)=det⁡(ϕ(A⊗B))$\det (A\otimes B)=\det \left(\varphi (A\otimes B)\right)$ for all d41318dbd148e5ef0" title="Click to view the MathML source">A∈H_m$A\in H_m$, B∈H_n$B\in H_n$. The connection of the problem to quantum information science is mentioned.