Constructing Mutually Unbiased Bases from Quantum Latin Squares

TL;DR

This paper introduces orthogonal quantum Latin squares and demonstrates how they can be used to construct mutually unbiased maximally entangled bases, offering a more general method than previous approaches.

Contribution

The paper presents a new framework using orthogonal quantum Latin squares to construct mutually unbiased bases in quantum information science.

Findings

Constructed mutually unbiased maximally entangled bases from quantum Latin squares.

Showed the new construction is more general than previous methods.

Compared new construction with Beth and Wocjan's approach, demonstrating advantages.

Abstract

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.