An All-But-One Entropic Uncertainty Relation, and Application to Password-Based Identification

Abstract

Entropic uncertainty relations are quantitative characterizations of Heisenberg’s uncertainty principle, which make use of an entropy measure to quantify uncertainty. We propose a new entropic uncertainty relation. It is the first such uncertainty relation that lower bounds the uncertainty in the measurement outcome for all but one choice for the measurement from an arbitrary (and in particular an arbitrarily large) set of possible measurements, and, at the same time, uses the min-entropy as entropy measure, rather than the Shannon entropy. This makes it especially suited for quantum cryptography.