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Quantum Foundations
Mutually Unbiased Bases in Composite Dimensions - A Review
arXiv
Authors: Daniel McNulty, Stefan Weigert
Year
2024
Paper ID
37387
Status
Preprint
Abstract Read
~2 min
Abstract Words
91
Citations
N/A
Abstract
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.
Why This Paper Matters
- This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
- It adds a 2024 reference point for readers tracking recent quantum research.
- Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications.
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