Security of quantum bit string commitment depends on the information measure

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dc.creatorBuhrman, Harry
dc.creatorChristandl, Matthias
dc.creatorHayden, Patrick
dc.creatorLo, Hoi-Kwong
dc.creatorWehner, Stephanie
dc.date2006-09-29
dc.date2006-11-09
dc.date.accessioned2026-07-07T07:37:47Z
dc.date.available2026-07-07T07:37:47Z
dc.descriptionUnconditionally 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.
dc.descriptionTo 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
dc.identifierhttps://arxiv.org/abs/quant-ph/0609237
dc.identifierhttp://arxiv.org/abs/quant-ph/0609237
dc.identifierPhys. Rev. Lett., 97, 250501 (2006)
dc.identifierdoi:10.1103/PhysRevLett.97.250501
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120893
dc.subjectQuantum Physics
dc.titleSecurity of quantum bit string commitment depends on the information measure
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