Schmidt-correlated states, Weak Schmidt decomposition and generalized Bell-basis related to Hadamard matrices

Bobo Hua, Shao-Ming Fei, Jürgen Jost, and Xianqing Li-Jost

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Submission date: 14. Aug. 2013 (revised version: January 2015)
Pages: 18
published in: Reports on mathematical physics, 74 (2014) 1, p. 89-103 
DOI number (of the published article): 10.1016/S0034-4877(14)60059-8
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Abstract:
We study the weak Schmidt decomposition which allows the Schmidt coefficients to be complex-valued. For a mixed state that is an ensemble of pure states which can be simultaneously diagonalized in weak Schmidt decomposition, we obtain a criterion of separability of the state. Furthermore, we introduce generalized Bell bases and explore their connections to Hadamard matrices and the separability criterion.