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

Yasuo Watatani

安男 綿谷

Yi-yang Song, Guijun Zhang, Lingshan Xu +1 more

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

Benjamin Musto

We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and show how a pair of mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum Latin squares. We also compare our construction to an existing construction due to Beth and Wocjan and show that ours is strictly more general.

Tomasz Paterek, M Paw Lowski, Markus Grassl +1 more

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 that has been shown to relate the two problems and generates complete sets of MUB in power-of-prime dimensions and three MUB 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.