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A new proof for the existence of mutually unbiased bases

Somshubhro Bandyopadhyay·P. Oscar Boykin·Vwani Roychowdhury·Farrokh Vatan
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Abstract

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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Somshubhro Bandyopadhyay, P. Oscar Boykin, Vwani Roychowdhury, Farrokh Vatan. 2001-09-07. A new proof for the existence of mutually unbiased bases. https://arxiv.org/abs/quant-ph/0103162

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