The Limited Role of Mutually Unbiased Product Bases in Dimension Six
Daniel McNulty, Stefan Weigert
TL;DR
This paper investigates the structure of mutually unbiased bases in six-dimensional quantum systems, demonstrating that a complete set cannot include more than one product basis, thus limiting their configuration.
Contribution
It proves that in dimension six, a complete set of mutually unbiased bases cannot have more than one product basis, clarifying their possible arrangements.
Findings
A complete set of seven mutually unbiased bases in dimension six cannot contain more than one product basis.
The result constrains the structure of mutually unbiased bases in composite dimensions.
Supports the conjecture about the scarcity of product bases in higher-dimensional quantum systems.
Abstract
We show that a complete set of seven mutually unbiased bases in dimension six, if it exists, cannot contain more than one product basis.
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