Mutually Unbiased Bases in Composite Dimensions -- A Review

Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power, i.e. in composite dimensions...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: McNulty, Daniel, Weigert, Stefan
Format: Article
Language:English
Subjects:
Hilbert space
Information theory
Quantum theory
Online Access:Get full text
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Summary:Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power, i.e. in composite dimensions such as six or ten. Fourteen mathematically equivalent formulations of the existence problem are presented. We comprehensively summarise analytic, computer-aided and numerical results relevant to the case of composite dimensions. Known modifications of the existence problem are reviewed and potential solution strategies are outlined.
ISSN:2331-8422