The problem of mutually unbiased bases in dimension 6

TL;DR

This paper discusses a discretization method to investigate the maximum number of mutually unbiased bases in six-dimensional quantum systems, addressing a long-standing open problem with initial findings.

Contribution

It introduces a discretization approach and key definitions to advance the understanding of mutually unbiased bases in dimension 6, providing preliminary results.

Findings

Proposed a discretization framework for the problem

Outlined key definitions and ideas for the approach

Presented initial results towards solving the open problem

Abstract

We outline a discretization approach to determine the maximal number of mutually unbiased bases in dimension 6. We describe the basic ideas and introduce the most important definitions to tackle this famous open problem which has been open for the last 10 years. Some preliminary results are also listed.