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Entropic uncertainty relations for incomplete sets of mutually unbiased observables

Adam Azarchs
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Abstract

Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases a more useful way to quantify incompatibility between observables. Of particular interest are relationships between `mutually unbiased' observables, which are maximally incompatible. Lower bounds on the sum of entropies for sets of two such observables, and for complete sets of observables within a space of given dimension, have been found. This paper explores relations in the intermediate regime of large, but far from complete, sets of unbiased observables.

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Adam Azarchs. 2004-12-10. Entropic uncertainty relations for incomplete sets of mutually unbiased observables. https://arxiv.org/abs/quant-ph/0412083

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