Article

# Hermitian Tensor Product Approximation of Complex Matrices and Separability

Capital Normal University, Peping, Beijing, China
(Impact Factor: 0.87). 04/2006; 57(2):271-288. DOI: 10.1016/S0034-4877(06)80021-2
Source: arXiv

ABSTRACT

The approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space $H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices on $H_1$ and $H_2$ is presented. From this construction the separability of quantum states is discussed. Comment: 16 pages

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Available from: Naihuan Jing, Dec 30, 2013
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• "Also, if {A 1 , ..., A n } and {B 1 , ..., B n } are linear independent sets then n i=1 A i ⊗ B i is a minimal Hermitian decomposition of A. Every Hermitian matrix has a minimal Hermitian decomposition. This result was proved in [5] but, here below, we present a quick proof for the convenience of the reader. "
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