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LINEAR MAPS PRESERVING TENSOR PRODUCTS OF RANK-ONE HERMITIAN MATRICES.
- Source :
-
Journal of the Australian Mathematical Society . Jun2015, Vol. 98 Issue 3, p407-428. 22p. - Publication Year :
- 2015
-
Abstract
- For a positive integer $n\geq 2$, let $M_{n}$ be the set of $n\times n$ complex matrices and $H_{n}$ the set of Hermitian matrices in $M_{n}$. We characterize injective linear maps ${\it\phi}:H_{m_{1}\cdots m_{l}}\rightarrow H_{n}$ satisfying $$\begin{eqnarray}\text{rank}(A_{1}\otimes \cdots \otimes A_{l})=1\Longrightarrow \text{rank}({\it\phi}(A_{1}\otimes \cdots \otimes A_{l}))=1\end{eqnarray}$$ for all $A_{k}\in H_{m_{k}}$, $k=1,\dots ,l$, where $l,m_{1},\dots ,m_{l}\geq 2$ are positive integers. The necessity of the injectivity assumption is shown. Moreover, the connection of the problem to quantum information science is mentioned. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14467887
- Volume :
- 98
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 102228931
- Full Text :
- https://doi.org/10.1017/S1446788714000603