Experimental Unconditionally Secure Bit Commitment

Quantum physics allows for unconditionally secure communication between parties that trust each other. However, when the parties do not trust each other such as in the bit commitment scenario, quantum physics is not enough to guarantee security unless extra assumptions are made. Unconditionally secure bit commitment only becomes feasible when quantum physics is combined with relativistic causality constraints. Here we experimentally implement a quantum bit commitment protocol with relativistic constraints that offers unconditional security. The commitment is made through quantum measurements in two quantum key distribution systems in which the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. In each run of the experiment, a bit is successfully committed with less than $5.68\times 10^{-2}$ cheating probability. This demonstrates the experimental feasibility of quantum communication with relativistic constraints.

Figure 1

(a) Diagram of the geographical distribution of the parties. The distance between Alice and Bob, and between $A_0$ and $B_0$ (and $A_1$ and $B_1$) is less than one meter. Alice communicates with her agents using sending and receiving telescopes. Each site has a global position system (GPS) for synchronization. (b) Diagram of Bob’s and Alice’s setup. Triggered by a GPS signal, Bob attenuates and encodes laser pulses with a BB84 [12] module, which is composed of two Wollason polarization prisms and a beam splitter, and sends them to Alice. Alice’s commitment setup consists of a half wave plate (HWP), a polarization beam splitter (PBS) and silicon avalanched photo-diode single photon detectors (SPDs). A field programmable gate array (FPGA) board is used to record the detected signals and communicate with Bob and Alice’s agents. Alice encodes, amplifies and sends the measurement results to her agents through telescopes. The four BB84 polarization states are denoted as $\text{}|H⟩\text{}$, $\text{}|V⟩\text{}$, $\text{}|\mathrm{+}⟩\text{}$, and $\text{}|\mathrm{-}⟩\text{}$. F.A.: fixed attenuator. OTM: optical transmission module. ORM: optical receiving module. EDFA: erbium-doped fiber amplifiers. APT: acquiring, pointing and tracking. (c) Diagram of $B_0$’s and $A_0$’s setup. The one of $B_1$ and $A_1$ is identical. $A_0$’s FPGA board receives and decrypts the detection information, stores it until the last classical signal is received, and then sends the measurement results to $B_0$. Bob’s agents record the timing of these signals and send the results to Bob.

Figure 2

Space-time diagram of the experiment. Alice can only have made her commitment in the intersection (shaded part) of $B_0$ and $B_1$’s past light cones, given that they have received the signals from $A_0$ and $A_1$. This area is in magenta in the figure. The latest time instant where Alice could have committed is given by $t_{\max }$; its projection in space lies on the line connecting $A_0$ with $A_1$.