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arxiv: quant-ph/0103162 · v3 · submitted 2001-03-29 · 🪐 quant-ph

A new proof for the existence of mutually unbiased bases

Somshubhro Bandyopadhyay , P. Oscar Boykin , Vwani Roychowdhury , Farrokh Vatan This is my paper
classification 🪐 quant-ph
keywords basesmutuallyunbiasedexistencedimensionmatricesproofcommuting
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We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2^m.

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  1. Mutually Unbiased Bases for Variational Quantum Initialization: Basis-Union Optimality and Adaptive Family Search

    quant-ph 2026-05 unverdicted novelty 7.0

    Complete MUB ensembles are optimal for isotropic Gaussian random-Hamiltonian width among d+1 basis unions, enabling adaptive MUB-XRot QAOA that is non-worse than standard QAOA in 80% of 1500 benchmark cases.