Optimality of entropic uncertainty relations

Understand

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal.

• Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties.
• In this work we establish optimal uncertainty relations by characterising the optimal lower bound in scenarios similar to the Maassen-Uffink type.
• We disprove a conjecture by Englert et al.