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.

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

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• Efficient Generation of Generic Entanglement
• Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
• Reexamination of Quantum Bit Commitment: the Possible and the Impossible
• Uncertainty Relation for the Discrete Fourier Transform
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Locking classical information
• Experimental quantum tossing of a single coin
• Impossibility of Growing Quantum Bit Commitments
• Quantum to Classical Randomness Extractors
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• Oblivious transfer based on quantum state computational distinguishability
• Quantum String Seal Is Insecure
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• Composable Security in the Bounded-Quantum-Storage Model
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