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Security of quantum bit string commitment depends on the information measure.

Harry Buhrman1, Matthias Christandl, Patrick Hayden

  • 1CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.

Physical Review Letters
|February 7, 2007
PubMed
Summary
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Quantum bit commitment, impossible classically and quantumly, faces new limits. Researchers show schemes where Alice can cheat on a bits and Bob learns b bits, finding a + b >= n under traditional security, but a = 4log2(n) + O(1) and b = 4 with accessible information criteria.

Area of Science:

  • Quantum Information Theory
  • Cryptography
  • Computer Science

Background:

  • Unconditionally secure nonrelativistic bit commitment is impossible in classical and quantum systems.
  • Existing research has explored limitations on bit commitment protocols.

Purpose of the Study:

  • To investigate the limits of quantum bit commitment schemes when committing to a string of n bits.
  • To analyze security criteria based on cheating probabilities and accessible information.

Main Methods:

  • Developed a framework for quantum bit commitment schemes.
  • Analyzed security using traditional criteria (cheating and guessing probabilities).
  • Analyzed security using a more liberal criterion (accessible information).

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Main Results:

  • Demonstrated that under traditional security criteria, a + b >= n, meaning no effective schemes exist.
  • Constructed quantum schemes with a more liberal security criterion where cheating (a) is limited to 4log2(n) + O(1) and accessible information (b) is 4.
  • Showcased that these results are classically impossible.

Conclusions:

  • The study significantly extends the known no-go results for quantum bit commitment.
  • Introduced new quantum schemes that push the boundaries of secure bit commitment.
  • Highlighted the importance of security criteria in evaluating quantum cryptographic protocols.