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Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power

Asha Rao, Diane M. Donovan, Joanne L. Hall

Cryptography and CommunicationsMay 31, 201010 citations

Mutually unbiased bases, Latin squares and orthogonal pairs (群論とその周辺--RIMS研究集会報告集)

安男綿谷

数理解析研究所講究録Jul 1, 20070 citations

Mutually unbiased bases, Latin squares and orthogonal pairs(Group Theory and Related Topics)

Yasuo Watatani

Jul 1, 20070 citations

Mutually unbiased bases, Latin squares and orthogonal pairs(Group Theory and Related Topics)

安男綿谷

数理解析研究所講究録Jul 1, 20070 citations

The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares

Iulia Ghiu, Cristian Ghiu

arXiv:1312.3236Reports on Mathematical PhysicsFeb 1, 20143 citations

New construction of mutually unbiased bases in square dimensions

Paweł Wocjan, T. Beth

We show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s^2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (s,k)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d=s^2 is greater than s^{1/14.8} for all s but finitely many exceptions. Furthermore, our construction gives more mutually unbiased bases in many non-prime-power dimensions than the construction that reduces the problem to prime power dimensions.We show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s^2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (s,k)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d=s^2 is greater than s^{1/14.8} for all s but finitely many exceptions. Furthermore, our construction gives more mutually unbiased bases in many non-prime-power dimensions than the construction that reduces the problem to prime power dimensions.

arXiv:quant-ph/0407081Quantum Information and ComputationMay 1, 2005106 citations

Construction of Mutually Unbiased Bases Using Mutually Orthogonal Latin Squares

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Construction of Mutually Unbiased Bases Using Mutually Orthogonal Latin Squares

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