Construction of special entangled basis based on generalized weighing matrices. (20th August 2019)

• Record Type: Journal Article
• Authors: Li, Mao-Sheng; Wang, Yan-Ling
• Is Part Of: Journal of physics. Volume 52:Number 37(2019)
• Publication Date: 2019-08-20
• Subjects: maximally entangled states -- special entangled basis -- skew Hadamard matrix -- generalized weighing matrices -- weighing matrices; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab331b
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.