Experimental Realization of Device-Independent Quantum Randomness Expansion

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\times {10}^8$ quantum-proof random bits while consuming $4.39\times {10}^8\mathrm{bits}$ of entropy, expanding our store of randomness by $1.08\times {10}^8\mathrm{bits}$ at a latency of about 13.1 h, with a total soundness error $4.6\times {10}^{-10}$. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

Figure 1

A schematic demonstration of the experimental setup. The untrusted quantum devices are colored in orange and circled with the dotted line. The trusted parts are colored in blue. Specifically, we make the following assumptions in the protocol: (1) Secure lab: The information exchange with an outside entity is controlled. The devices cannot communicate to the outside to leak the experimental results directly. (2) Nonsignaling condition: In each trial, the measurement process of Alice and Bob is independent of the other party. (3) Trusted coordinator: A well characterized biased random number generator (depicted by “Biased QRNG” in the figure) determines a trial to be “spot” or “checking.” The setting is private to the measurement devices and the entanglement source. (4) Trusted inputs: Alice and Bob each have a private random number generator (depicted by “Unbiased QRNG” in the figure) to feed perfect random bits to the measurement device in the “checking trials.” (5) Trusted postprocessors: The classical postprocessing procedure is trusted. (6) Quantum mechanism: Quantum mechanics is correct and complete.

Figure 2

Randomness expansion of at least $k_{\exp }=512$ random bits in at most $N=2.35\times {10}^{11}$ trials with a smoothing parameter ${ϵ}_h=2^{-32}$ in randomness generation. Blue dotted line: the experimental amount of generated ${ϵ}_h$-smooth min-entropy witnessed by the QEF by the $n$th trial $R_n$; black solid line: the amount of entropy consumed by the $n$th trial $k_0+n{r}_{\mathrm{in}}$; yellow dash line: the least amount of ${ϵ}_h$-smooth min-entropy required to be generated for a successful randomness expansion task. Surpassing the threshold before $N$ trials guarantees a successful randomness expansion of at least 512 near-uniform random bits at the end of the protocol, otherwise the protocol fails (represented by the gray area). The open square denotes the largest allowed number of trials and the open circle denotes the actual number of trials to accomplish the task. We note that the experiment can be stopped in advance at the $N_{\mathrm{act}}$th trial. Still, we continue the experiment for a longer period to show the robustness of the experimental setup, as shown in the shaded area (in all, we have accumulated data of approximately $3\times {10}^{12}$ trials).