Construction of special entangled basis based on generalized weighing matrices

A special entangled basis (SEBk) is a set with orthonormal entangled pure states in whose nonzero Schmidt coefficients are all equal to . When k is equal to the minimum of d and , we get a maximally entangled basis. In this paper, we present how to construct a special entangled basis via some specia...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 52; no. 37; pp. 375303 - 375320
Main Authors Li, Mao-Sheng, Wang, Yan-Ling
Format Journal Article
LanguageEnglish
Published IOP Publishing 13.09.2019
Subjects
generalized weighing matrices
maximally entangled states
skew Hadamard matrix
special entangled basis
weighing matrices
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Summary:A special entangled basis (SEBk) is a set with orthonormal entangled pure states in whose nonzero Schmidt coefficients are all equal to . When k is equal to the minimum of d and , we get a maximally entangled basis. In this paper, we present how to construct a special entangled basis via some special matrices which are known as weighing matrices. Specifically, using a skew Hadamard matrix of order k  +  1, we derive a weighing matrix that is useful for constructing SEBk in whenever . These results are further progress of those studied by Guo et al (2015 J. Phys. A: Math. Theor. 48 245301). We also disprove two conjectures proposed by them.
Bibliography:JPhysA-111426.R2
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab331b