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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
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.