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Security of quantum bit string commitment depends on the information measure

Harry Buhrman·Matthias Christandl·Patrick Hayden·Hoi-Kwong Lo·Stephanie Wehner
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Abstract

Unconditionally secure non-relativistic bit commitment is known to be impossible in both the classical and the quantum world. However, when committing to a string of n bits at once, how far can we stretch the quantum limits? In this letter, we introduce a framework of quantum schemes where Alice commits a string of n bits to Bob, in such a way that she can only cheat on a bits and Bob can learn at most b bits of information before the reveal phase. Our results are two-fold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: a+b is at least n. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where a=4 log n+O(1) and b=4, which is impossible classically. Our findings significantly extend known no-go results for quantum bit commitment.

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Harry Buhrman, Matthias Christandl, Patrick Hayden, Hoi-Kwong Lo, Stephanie Wehner. 2006-11-09. Security of quantum bit string commitment depends on the information measure. https://doi.org/10.1103/physrevlett.97.250501

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