skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum bit commitment with misaligned reference frames

Abstract

Suppose that Alice and Bob define their coordinate axes differently, and the change of reference frame between them is given by a probability distribution {mu} over SO(3). We show that this uncertainty of reference frame is of no use for bit commitment when {mu} is uniformly distributed over a (sub)group of SO(3), but other choices of {mu} can give rise to a partially or even arbitrarily secure bit commitment.

Authors:
 [1]; ;  [2]
  1. Department of Physics, MIT, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 (United States) and Department of Computer Science, University of Bristol, Bristol BS8 1UB (United Kingdom)
  2. IBM Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598 (United States)
Publication Date:
OSTI Identifier:
20786860
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.032311; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; COORDINATES; DISTRIBUTION; INFORMATION THEORY; PROBABILITY; QUANTUM CRYPTOGRAPHY; QUANTUM MECHANICS; QUBITS; SECRECY PROTECTION; SO-3 GROUPS

Citation Formats

Harrow, Aram, Oliveira, Roberto, and Terhal, Barbara M. Quantum bit commitment with misaligned reference frames. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Harrow, Aram, Oliveira, Roberto, & Terhal, Barbara M. Quantum bit commitment with misaligned reference frames. United States. doi:10.1103/PHYSREVA.73.0.
Harrow, Aram, Oliveira, Roberto, and Terhal, Barbara M. Wed . "Quantum bit commitment with misaligned reference frames". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786860,
title = {Quantum bit commitment with misaligned reference frames},
author = {Harrow, Aram and Oliveira, Roberto and Terhal, Barbara M.},
abstractNote = {Suppose that Alice and Bob define their coordinate axes differently, and the change of reference frame between them is given by a probability distribution {mu} over SO(3). We show that this uncertainty of reference frame is of no use for bit commitment when {mu} is uniformly distributed over a (sub)group of SO(3), but other choices of {mu} can give rise to a partially or even arbitrarily secure bit commitment.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • In this paper we focus on a special framework for quantum coin-flipping protocols, bit-commitment-based protocols, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyze a sequence of multiround protocols that tries to overcome the drawbacks of the previously proposed protocols in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a more clever proof technique maymore » be required to show this optimality.« less
  • Quantum protocols for coin flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with cheat sensitivity as well, and is used to derive two results: There are no quantum strong coin-flipping protocols with cheat sensitivity that is linear in the bias (or bit-commitment protocols with linear cheat detection) because these can be composed to produce strong coin flipping with arbitrarily small bias. On the other hand, it appears that quadratic cheat detection cannot be composed in series tomore » obtain even weak coin flipping with arbitrarily small bias.« less
  • Quantum-bit-string commitment [A. Kent, Phys. Rev. Lett. 90, 237901 (2003)] (QBSC) is a variant of bit commitment (BC). In this paper, we propose a QBSC protocol that can be implemented using currently available technology and prove its security under the same security criteria as discussed by Kent. QBSC is a generalization of BC, but has slightly weaker requirements, and our proposed protocol is not intended to break the no-go theorem of quantum BC.
  • The existence of unconditionally secure quantum bit commitment (QBC) is excluded by the Mayers-Lo-Chau no-go theorem. Here we look for the second-best: a QBC protocol that can defeat certain quantum attacks. By breaking the knowledge symmetry between the participants with quantum algorithm, a QBC protocol is proposed and is proven to be secure against a major kind of coherent attacks - the dummy attack, in which the participant makes an empty promise instead of committing to a specific bit. Therefore it surpasses previous QBC protocols which are secure against individual attacks only.
  • Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. We give a strengthened and explicit proof of this result. We extend its scope to a much larger variety of protocols, which may have an arbitrary number of rounds, in which both classical and quantum information is exchanged, and which may include aborts and resets. Moreover, we do not consider the receiver to be bound to a fixed 'honest' strategy, so that 'anonymous state protocols', which were recently suggested as a possible way to beat the known no-go results, aremore » also covered. We show that any concealing protocol allows the sender to find a cheating strategy, which is universal in the sense that it works against any strategy of the receiver. Moreover, if the concealing property holds only approximately, the cheat goes undetected with a high probability, which we explicitly estimate. The proof uses an explicit formalization of general two-party protocols, which is applicable to more general situations, and an estimate about the continuity of the Stinespring dilation of a general quantum channel. The result also provides a natural characterization of protocols that fall outside the standard setting of unlimited available technology and thus may allow secure bit commitment. We present such a protocol whose security, perhaps surprisingly, relies on decoherence in the receiver's laboratory.« less