Construction of Mutually Unbiased Bases Using Mutually Orthogonal Latin Squares

Using character of mutually orthogonal Latin squares, we first prove that two special squares are orthogonal to a complete set of mutually orthogonal Latin squares of order d . Then using the complete set of mutually orthogonal Latin squares of order d and two special squares, we construct d + 1 mut...

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Bibliographic Details
Published in:International journal of theoretical physics 2020-06, Vol.59 (6), p.1777-1787
Main Authors: Song, Yi-yang, Zhang, Gui-jun, Xu, Ling-shan, Tao, Yuan-hong
Format: Article
Language:English
Subjects:
Arrays
Elementary Particles
Latin square design
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Theoretical
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Summary:Using character of mutually orthogonal Latin squares, we first prove that two special squares are orthogonal to a complete set of mutually orthogonal Latin squares of order d . Then using the complete set of mutually orthogonal Latin squares of order d and two special squares, we construct d + 1 mutually unbiased bases in ℂ d ⊗ ℂ d , which include d − 1 mutually unbiased maximally entangled bases and two mutually unbiased product bases. We also present the corresponding construction in ℂ 3 ⊗ ℂ 3 , ℂ 4 ⊗ ℂ 4 and ℂ 5 ⊗ ℂ 5 .
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-020-04444-x