Tight Entropic Uncertainty Relations

• URL: http://arxiv.org/abs/2605.01832v1
• Date: Sun, 03 May 2026 11:57:25 GMT
• Title: Tight Entropic Uncertainty Relations
• Abstract summary: Entropic uncertainty relations $H(A)+H(B)geqslant $ give a nonzero lower bound $$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$.<n>They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $$ typically are state independent.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entropic uncertainty relations $H(A)+H(B)\geqslant γ$ give a nonzero lower bound $γ$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $γ$ typically are state independent. Here we provide a state-independent lower bound $γ_s$ that is better than the textbook Maassen-Uffink bound and, in the limit of the parameter $s\to 2$, becomes asymptotically tight for all $A,B$. The bound can be extended to Renyi entropies.

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