Quantum Inf Process (2014) 13:2195–2211
Simpliﬁed quantum bit commitment using single
Guang Ping He
Received: 12 April 2013 / Accepted: 3 January 2014 / Published online: 16 January 2014
© Springer Science+Business Media New York 2014
Abstract We simpliﬁed our previously proposed quantum bit commitment (QBC)
protocol based on the Mach–Zehnder interferometer, by replacing symmetric beam
splitters with asymmetric ones. It eliminates the need for random sending time of the
photons; thus, the feasibility and efﬁciency are both improved. The protocol is immune
to the cheating strategy in the Mayers-Lo-Chau no-go theorem of unconditionally
secure QBC, because the density matrices of the committed states do not satisfy a
crucial condition on which the no-go theorem holds.
Keywords Quantum cryptography · Quantum bit commitment · Quantum key
distribution · Quantum nonlocality
Quantum bit commitment (QBC) [1,2] is a two-party cryptography including two
phases. In the commit phase, Alice (the sender of the commitment) decides the value
of the bit b (b = 0 or 1) that she wants to commit, and sends Bob (the receiver
of the commitment) a piece of evidence, e.g., some quantum states. Later, in the
unveil phase, Alice announces the value of b, and Bob checks it with the evidence.
An unconditionally secure QBC protocol needs to be both binding (i.e., Alice cannot
change the value of b after the commit phase) and concealing (Bob cannot know b
before the unveil phase) without relying on any computational assumption.
This work was supported in part by the NSF of China, the NSF of Guangdong Province, and the
Foundation of Zhongshan University Advanced Research Center.
G. P. He (
School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, China