Linear maps preserving determinant of tensor products of Hermitian matrices

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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 \geq 2

be positive integers and let H_n

H_{n}

be the set of n×n

n \times n

complex Hermitian matrices. We study linear maps ϕ:H_mn→H_mn

ϕ : H_{m n} \to H_{m n}

satisfying det⁡(A⊗B)=det⁡(ϕ(A⊗B))

\det (A \otimes B) = \det (ϕ (A \otimes B))

for all 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.

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