title: Security of quantum bit string commitment depends on the information measure.
abstract: Unconditionally secure nonrelativistic 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 twofold: 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 = 4log2(n) + O(1) and b = 4, which is impossible classically. Our findings significantly extend known no-go results for quantum bit commitment.
authors.affiliation: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.
authors.forename: Harry
authors.initials: H
authors.lastname: Buhrman
authors.forename: Matthias
authors.initials: M
authors.lastname: Christandl
authors.forename: Patrick
authors.initials: P
authors.lastname: Hayden
authors.forename: Hoi-Kwong
authors.initials: HK
authors.lastname: Lo
authors.forename: Stephanie
authors.initials: S
authors.lastname: Wehner