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arXiv · 1109.0060

Mutually unbiased bases for quantum states defined over p-adic numbers

Wim van Dam·Alexander Russell
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Abstract

We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known. We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces.

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Wim van Dam, Alexander Russell. 2011-09-01. Mutually unbiased bases for quantum states defined over p-adic numbers. https://arxiv.org/abs/1109.0060

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