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Q: Fachverband Quantenoptik und Photonik

Q 47: Quanteninformation (Quantenkommunikation)

Q 47.4: Talk

Wednesday, March 21, 2007, 17:15–17:30, 5L

Private States, Privacy Amplification, and the Uncertainty Principle in Quantum Cryptography — •Joseph Renes¹ and Jean-Christian Boileau^2,3 — ¹Institut für Angewandte Physik, TU Darmstadt, Darmstadt, Germany — ²Institute for Quantum Computation, University of Waterloo, Waterloo, Canada — ³Perimeter Institute for Theoretical Physics, Waterloo, Canada

Quantum cryptography has typically dealt with the problem of extracting a secret key from a partially private string in one of three ways, corresponding to different treatment of the parties to the cryptographic protocol. Use of two-universal hash functions, termed classical privacy amplification, comes from considering the eavesdropper's quantum state. Alternatively, focusing on the state held by the honest parties can be done either concretely in private state distillation or abstractly as in the approach based on the uncertainty principle. We show that these three are equivalent and interchangeable, unifying the corresponding security proofs of quantum key distribution. By adapting the security proof based on the uncertainty principle, we construct a new protocol for private state distillation which we then prove is identical to classical privacy amplification. Underlying this approach is a new characterization of private states, quantum states capable of generating a secret key, whose relation to their standard formulation is again understood as an instance of the uncertainty principle: A key corresponding to measurement of a given observable is private when the honest parties have full knowledge of the conjugate observable.