dorsal/arxiv
View SchemaSecurity of quantum bit string commitment depends on the information measure
| Authors | Harry Buhrman, Matthias Christandl, Patrick Hayden, Hoi-Kwong Lo, Stephanie Wehner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609237 |
| URL | https://arxiv.org/abs/quant-ph/0609237 |
| DOI | 10.1103/PhysRevLett.97.250501 |
| Journal | Phys. Rev. Lett., 97, 250501 (2006) |
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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"abstract": "Unconditionally secure non-relativistic bit commitment is known to be\nimpossible in both the classical and the quantum world. However, when\ncommitting to a string of n bits at once, how far can we stretch the quantum\nlimits? In this letter, we introduce a framework of quantum schemes where Alice\ncommits a string of n bits to Bob, in such a way that she can only cheat on a\nbits and Bob can learn at most b bits of information before the reveal phase.\nOur results are two-fold: we show by an explicit construction that in the\ntraditional approach, where the reveal and guess probabilities form the\nsecurity criteria, no good schemes can exist: a+b is at least n. If, however,\nwe use a more liberal criterion of security, the accessible information, we\nconstruct schemes where a=4 log n+O(1) and b=4, which is impossible\nclassically. Our findings significantly extend known no-go results for quantum\nbit commitment.",
"arxiv_id": "quant-ph/0609237",
"authors": [
"Harry Buhrman",
"Matthias Christandl",
"Patrick Hayden",
"Hoi-Kwong Lo",
"Stephanie Wehner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.97.250501",
"journal_ref": "Phys. Rev. Lett., 97, 250501 (2006)",
"title": "Security of quantum bit string commitment depends on the information measure",
"url": "https://arxiv.org/abs/quant-ph/0609237"
},
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