A Tight High-Order Entropic Quantum Uncertainty Relation with Applications

  • Ivan B. Damgård
  • Serge Fehr
  • Renato Renner
  • Louis Salvail
  • Christian Schaffner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4622)


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% can be tolerated (compared to 13% in the standard model).

Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.


Hash Function Uncertainty Relation Quantum Channel Shannon Entropy Commitment Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ivan B. Damgård
    • 1
  • Serge Fehr
    • 2
  • Renato Renner
    • 3
  • Louis Salvail
    • 1
  • Christian Schaffner
    • 2
  1. 1.Basic Research in Computer Science (BRICS), funded by the Danish National Research Foundation, Department of Computer Science, University of AarhusDenmark
  2. 2.Center for Mathematics and Computer Science (CWI), AmsterdamNetherlands
  3. 3.Cambridge UniversityUK

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