# Information Security and Cryptography Research Group

## A Tight High-Order Entropic Quantum Uncertainty Relation With Applications

### Ivan Damgård, Serge Fehr, Renato Renner, Louis Salvail, and Christian Schaffner

Dec 2006, Available at http://arxiv.org/abs/quant-ph/0612014.

We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded quantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17 in the standard model).

## BibTeX Citation

@unpublished{DFRSS06,
author       = {Ivan Damgård and Serge Fehr and Renato Renner and Louis Salvail and Christian Schaffner},
title        = {A Tight High-Order Entropic Quantum Uncertainty Relation With Applications},
year         = 2006,
month        = 12,
note         = {Available at http://arxiv.org/abs/quant-ph/0612014},
}