Emanuel Knill

With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all previous experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is used. Here, we devise a device-independent spot-checking protocol which uses only uniform bits as input. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237 bits) than consumed input bits (953,301,640 bits), which is 5 orders of magnitude more efficient than our previous work [Phys. Rev. Lett. 124, 010505 (2020)]. The experiment ran for 91.0 hours, creating randomness at an average rate of 3,606 bits/second with a soundness error bounded by 5.7e-7 in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and the protocol may one day enable high-quality sources of private randomness as the device footprint shrinks.

Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. Here we develop a broadly applicable framework, quantum probability estimation, for yielding efficient quantum-proof protocols. The framework is general and encompasses methods from previous works [Miller and Shi, SIAM Journal on Computing 46, 1304 (2017); Arnon-Friedman et al., Nature Communications 9, 459 (2018)]. Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution. Moreover, we demonstrate device-independent quantum randomness generation from a loophole-free Bell test with quantum probability estimation, obtaining multiple blocks of 512 random bits with an average experiment time of less than 5 minutes per block and with certified error bounded by $2^{-64}\approx 5.42\times 10^{-20}$.

The reliability of quantum resources can be compromised in practice due to the complexity of their generation processes and/or the potential manipulations by untrusted parties during transmission. When performing an information task with an unreliable quantum resource, it is incorrect to treat the random variables associated with repeated experimental trials as independent and identically distributed (i.i.d.). To certify the performance of such a task, one can make a random decision in each trial, either to spot-check some property of the quantum resource or to utilize the resource for the task. The task considered can be quantum key distribution, quantum randomness expansion, verifiable quantum computation, or resource allocation in quantum networks. Unfortunately, existing methods for certifying quantum performance through spot-checking are not suitable for non-i.i.d. repeated trials without additional assumptions. Here we present a novel method to address this challenge. The method works efficiently with a finite number of non-i.i.d. trials. Furthermore, our method can be adapted to estimate quantum properties in situations where the quantum resource is spot-checked and destroyed by a measurement during each non-i.i.d. repeated trial.