Limits on the ability of quantum states to convey classical messages

  • Authors:
  • Ashwin Nayak;Julia Salzman

  • Affiliations:
  • Institute for Quantum Computing, University of Waterloo, and Perimeter Institute for Theoretical Physics, Waterloo, Ont., Canada;Stanford University, Stanford, California

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2006

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Abstract

We revisit the problem of conveying classical messages by transmitting quantum states, and derive new, optimal bounds on the number of quantum bits required for this task. Much of the previous work on this problem, and on other communication tasks in the setting of bounded error entanglement-assisted communication, is based on sophisticated information theoretic arguments. Our results are derived from first principles, using a simple linear algebraic technique. A direct consequence is a tight lower bound for the Inner Product function that has found applications to privacy amplification in quantum key distribution protocols.