On the connection between mutually unbiased bases and orthogonal Latin squares

Abstract

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.

6 pages, submitted to Proceedings of CEWQO 2009

References in corpus (5)

• A new proof for the existence of mutually unbiased bases
• Mubs and Hadamards of Order Six
• Mutually Unbiased Bases and Finite Projective Planes
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• The limitations of nice mutually unbiased bases

Cited by in corpus (7)

• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Construction of mutually unbiased bases with cyclic symmetry for qubit systems
• Quantum combinatorial designs and $k$-uniform states
• Small sets of complementary observables
• Optimal quantum tomography with constrained elementary measurements arising from unitary bases
• The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares
• Discrete phase-space approach to mutually orthogonal Latin squares