Quantum Information Processing, Vol. 5, No. 2, April 2006 (© 2006)
The Physics of No-Bit-Commitment: Generalized
Quantum Non-Locality Versus Oblivious Transfer
Anthony J. Short,
and Sandu Popescu
Received December 23, 2005; accepted March 7, 2006; Published online April 22, 2006
We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030)
on oblivious transfer apparently opens the possibility that non-local correlations
which are stronger than those in quantum mechanics could be used for bit-
commitment. This is surprising, because it is the very existence of non-local cor-
relations which in quantum mechanics prevents bit-commitment. We resolve this
apparent paradox by stressing the difference between non-local correlations and
oblivious transfer, based on the time-ordering of their inputs and outputs, which
KEY WORDS: Quantum non-locality; bit-commitment; oblivious transfer;
PACS: 03.65.Ud; 03.67.Dd.
In 1984, Bennett and Brassard
proposed a quantum physics scheme
(BB84) by which two parties can establish a secret key, allowing them
to communicate with unconditional security against eavesdroppers. This
result remains one of the cornerstones of quantum cryptography, and gave
rise to the hope that many other cryptographic primitives (which clas-
sically rely on unprovable assumptions), could be made unconditionally
secure within a quantum framework. Perhaps the best known of these is
A bit-commitment scheme allows one party (Alice) to commit to a
decision in such a way as a second party (Bob) will believe her when
HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK.
Group of Applied Physics, University of Geneva, 20 rue de l’Ecole-de-m
Geneva 4, Switzerland.
Hewlett-Packard Laboratories, Stoke Gifford, Bristol BS12 6QZ, UK.
To whom correspondence should be addressed. E-mail: Tony.Short@bristol.ac.uk
1570-0755/06/0400-0131/0 © 2006 Springer Science+Business Media, Inc.