

Preprint 88/2013
Lower Bound of Concurrence Based on Generalized Positive Maps
Hui-Hui Qin and Shao-Ming Fei
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Submission date: 19. Aug. 2013 (revised version: January 2015)
Pages: 12
published in: Communications in theoretical physics, 60 (2013) 6, p. 663-666
DOI number (of the published article): 10.1088/0253-6102/60/6/05
Bibtex
PACS-Numbers: 03.67.Mn, 03.67.-a, 02.20.Hj, 03.65.-w
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Abstract:
We study the mathematical structures and relations among some quantities in the theory
of quantum entanglement, such as separability, weak Schmidt decompositions, Hadamard matrices
etc. We provide an operational method to identify the Schmidt-correlated states by using
weak Schmidt decomposition. We show that a mixed state is Schmidt-correlated if and only
if its spectral decomposition consists of a set of pure eigenstates which can be simultaneously
diagonalized in weak Schmidt decomposition, i.e. allowing for complex-valued diagonal
entries. For such states, the separability is reduced to the orthogonality conditions of the
vectors consisting of diagonal entries associated to the eigenstates; moreover, for a special
subclass of these states this is surprisingly related to the so-called complex Hadamard matrices.
Using the Hadamard matrices, we provide a variety of generalized maximal entangled Bell
bases.