A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
Ivan Damg{å}rd and Serge Fehr and Renato Renner and Louis Salvail and Christian Schaffner
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).