Mutually Unbiased Bases in Composite Dimensions -- A Review

• URL: http://arxiv.org/abs/2410.23997v1
• Date: Thu, 31 Oct 2024 14:58:00 GMT
• Title: Mutually Unbiased Bases in Composite Dimensions -- A Review
• Authors: Daniel McNulty, Stefan Weigert,
• Abstract summary: It remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of dimensions different from a prime power. Fourteen mathematically equivalent formulations of the existence problem are presented.
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• 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.

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