Jun Zhang

The ability to produce random numbers that are unknown to any outside party is crucial for many applications. Device-independent randomness generation (DIRNG) allows new randomness to be provably generated, without needing to trust the devices used for the protocol. This provides strong guarantees about the security of the output, but comes at the price of requiring the violation of a Bell inequality to implement. A further challenge is to make the bounds in the security proofs tight enough to allow expansion with contemporary technology. Thus, while randomness has been generated in recent experiments, the amount of randomness consumed in doing so has been too high to certify expansion based on existing theory. Here we present an experiment that demonstrates device-independent randomness expansion (DIRNE), i.e., where the generated randomness surpasses that consumed. By developing a loophole-free Bell test setup with a single photon detection efficiency of around 81% and exploiting a spot-checking protocol, we achieve a net gain of 2.63 × 10^8 certified bits with soundness error 5.74×10^{−8}. The experiment ran for 220 hours corresponding to an average rate of randomness generation of 8202 bits/s. By developing the Entropy Accumulation Theorem (EAT), we established security against quantum adversaries. We anticipate that this work will lead to further improvements that push device-independence towards commercial viability.

Recent advances in loophole-free Bell tests have profoundly impacted quantum cryptography, yet their security assumes trusted random number generators (RNGs) for measurement choices—a vulnerability termed the freedom-of-choice loophole. Here, we demonstrate that classical systems can spoof Bell violations under ostensibly loophole-free conditions using compromised RNGs. By synchronizing laser-generated separable states with imperfect RNG outputs in an optical setup, we simulate a CHSH test closing locality and detection loopholes. With full RNG access, we achieve a near-maximal CHSH value of 3.99, exceeding quantum limits. Crucially, partial RNG knowledge suffices: predetermining 10.6% of bits reproduces our “loophole free” optical system's CHSH value of 2.007, while Santha-Vazirani generators with 0.38-biased bits enable optimal spoofing. Even weakly correlated RNGs coordinated via entangled states—deviating by 0.04 from independence—allow violations. Prediction-based ratio analysis gives a P-value upper bound of 10^(-18266), misleadingly implying non-classicality if RNG flaws are ignored. Strikingly, we extract "device-independent" random bits from simulated outcomes, mirroring cryptographic protocols. This exposes a critical flaw: compromised input randomness invalidates security guarantees in Bell-inequality-based cryptography. Our findings mandate rigorous verification of both RNG integrity and Bell violations to ensure quantum cryptographic security.