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.

As application, we propose a new quantum identification scheme in the bounded-quantum-storage model. It makes use of our new uncertainty relation at the core of its security proof. In contrast to the original quantum identification scheme proposed by Damgård et al. [4], our new scheme also offers some security in case the bounded-quantum-storage assumption fails to hold. Specifically, our scheme remains secure against an adversary that has unbounded storage capabilities but is restricted to (non-adaptive) single-qubit operations. The scheme by Damgård et al., on the other hand, completely breaks down under such an attack.