Experimental Bit Commitment Based on Quantum Communication and Special Relativity

Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit a secret bit to Alice. Perfectly secure bit commitment between two mistrustful parties is impossible through asynchronous exchange of quantum information. Perfect security is however possible when Alice and Bob split into several agents exchanging classical and quantum information at times and locations suitably chosen to satisfy specific relativistic constraints. Here we report on an implementation of a bit commitment protocol using quantum communication and special relativity. Our protocol is based on [A. Kent, Phys. Rev. Lett. 109, 130501 (2012)] and has the advantage that it is practically feasible with arbitrary large separations between the agents in order to maximize the commitment time. By positioning agents in Geneva and Singapore, we obtain a commitment time of 15 ms. A security analysis considering experimental imperfections and finite statistics is presented.

Figure 1

(a) Space-time ($x\mathrm{\text{−}}t$) diagram of the protocol of Ref. 18. (b) The relativistic portion of a modified version of (a). The quantum exchange between Alice and Bob happens much before and is not shown.

Figure 2

Experimental setup located in Geneva. The setup located in Singapore is the same except for $A_1$ and $B_1$ that are replaced by $A_2$ and $B_2$, and that there is no QKD system.

Figure 3

Histogram of the observed QBER from the set of 50 commitments with measurement basis $b=0$. Inset: the circle, diamond and square points are experimental values of $p_{\det }$ corresponding to the highest, average, and lowest values of the set (all for the same value of $\mu$). The solid line is the boundary of the region for which our proof guarantees security (left side) in the asymptotic limit [Eq. (1)]. The uncertainty on $\mu$ corresponds to slightly overestimated daily fluctuations.