Exponential separations for one-way quantum communication complexity, with applications to cryptography

  • Authors:
  • Dmitry Gavinsky;Julia Kempe;Iordanis Kerenidis;Ran Raz;Ronald de Wolf

  • Affiliations:
  • University of Waterloo, Waterloo, Canada;Univ. Paris-Sud: Orsay and Tel Aviv Univ., Tel-Aviv, Israel;Univ. Paris-Sud: Orsay, Paris, France;Weizmann Institute, Rehovot, Israel;CWI, Amsterdam, Netherlands

  • Venue:
  • Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
  • Year:
  • 2007

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Abstract

We give an exponential separation between one-way quantum and classical communication protocols for twopartial Boolean functions, both of which are variants of the Boolean Hidden Matching Problem of Bar-Yossef et al. Earlier such an exponential separation was known only for a relational version of the Hidden Matching Problem. Our proofs use the Fourier coefficients inequality of Kahn, Kalai, and Linial. We give a number of applications of this separation. In particular, in the bounded-storage model of cryptography we exhibita scheme that is secure against adversaries with a certain amount of classical storage, but insecure against adversaries with a similar (or even much smaller) amount of quantum storage; in the setting of privacy amplification, we show that there are strong extractors that yield a classically secure key, but are insecure against a quantum adversary.