Security of quantum bit string commitment depends on the information measure
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.
Keywords
Cite
@article{arxiv.quant-ph/0609237,
title = {Security of quantum bit string commitment depends on the information measure},
author = {Harry Buhrman and Matthias Christandl and Patrick Hayden and Hoi-Kwong Lo and Stephanie Wehner},
journal= {arXiv preprint arXiv:quant-ph/0609237},
year = {2007}
}
Comments
To appear in PRL. Short version of quant-ph/0504078, long version to appear separately. Improved security definition and result, one new lemma that may be of independent interest. v2: added funding reference, no other changes