Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes

We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen Bennett-Brassard 1984 (BB84) qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at (or near) light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The protocol’s security relies only on simple properties of quantum information and the impossibility of superluminal signalling.

Figure 1

A nonideal implementation of the protocol in $1+1$ dimensions. (Not to scale.) Alice and Bob control disjoint regions of space-time, representing their respective secure laboratories. Bob generates random BB84 quantum states at $P^{\prime }$ and sends them (dashed arrow) to Alice at point $P$, where she measures them in her chosen basis. She reports the results (solid arrows) via secure classical (near) light-speed channels to her agents at the points $Q_i$, who relay them (dotted arrows) to Bob’s agents at the nearby points $Q_i^{\prime }$.