Experimental bit commitment based on quantum communication and special relativity

Abstract: Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit a secret bit to Alice. Perfectly secure bit commitment has been proven impossible through asynchronous exchange of classical and quantum information. Perfect security is however possible by restraining the exchange of classical and quantum information to suitably chosen relativistic constraints. This requires Alice (and Bob) to split into two remote agents performing space-like separated classical communication, and in one agent exchanging quantum bits with the other party. The duration of the commitment is given by the distance between the two remote agents. The original protocol requires the quantum communication to happen at a precise location and time with respect to the classical communication. We show how the protocol can be modified to relax this constraint such that the quantum part of the protocol can be performed at any time before the actual commitment, making it much more practical. Finally, we present an experimental demonstration of this protocol realized with a commercial quantum key distribution system and with synchronized classical agents located in Geneva and Singapore, yielding a commitment time of 15 ms. Our work includes a complete security analysis, accounting for experimental imperfections (multi-photon emission, transmission loss, detector inefficiency and dark counts) and finite statistics.