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. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2−64≈5.42×10−20.

1 aZhang, Yanbao1 aShalm, Lynden, K.1 aBienfang, Joshua, C.1 aStevens, Martin, J.1 aMazurek, Michael, D.1 aNam, Sae, Woo1 aAbellán, Carlos1 aAmaya, Waldimar1 aMitchell, Morgan, W.1 aFu, Honghao1 aMiller, Carl, A.1 aMink, Alan1 aKnill, Emanuel uhttps://arxiv.org/abs/1812.0778601139nas a2200133 4500008004100000245004700041210004600088260001200134300001100146520077800157100001600935700001700951856003700968 2018 eng d00aLocal randomness: Examples and application0 aLocal randomness Examples and application c03/2018 a0323243 aWhen two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

1 aFu, Honghao1 aMiller, Carl uhttps://arxiv.org/abs/1708.0433802310nas a2200121 4500008004100000245008000041210006900121520190800190100001902098700001802117700001602135856003702151 2018 eng d00aQuantum Probability Estimation for Randomness with Quantum Side Information0 aQuantum Probability Estimation for Randomness with Quantum Side 3 aWe develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability estimation (QPE). This includes asymptotic optimality at constant error and randomness expansion with logarithmic input entropy. QPE is implemented by constructing model-dependent quantum estimation factors (QEFs), which yield statistical confidence upper bounds on data-conditional normalized Rényi powers. This leads to conditional min-entropy estimates for randomness generation. The bounds are valid for relevant models of sequences of experimental trials without requiring independent and identical or stationary behavior. QEFs may be adapted to changing conditions during the sequence and trials can be stopped any time, such as when the results so far are satisfactory. QEFs can be constructed from entropy estimators to improve the bounds for conditional min-entropy of classical-quantum states from the entropy accumulation framework [Dupuis, Fawzi and Renner, arXiv:1607.01796]. QEFs are applicable to a larger class of models, including models permitting measurement devices with super-quantum but non-signaling behaviors and semi-device dependent models. The improved bounds are relevant for finite data or error bounds of the form e−κs, where s is the number of random bits produced. We give a general construction of entropy estimators based on maximum probability estimators, which exist for many configurations. For the class of (k,2,2) Bell-test configurations we provide schemas for directly optimizing QEFs to overcome the limitations of entropy-estimator-based constructions. We obtain and apply QEFs for examples involving the (2,2,2) Bell-test configuration to demonstrate substantial improvements in finite-data efficiency.

1 aKnill, Emanuel1 aZhang, Yanbao1 aFu, Honghao uhttps://arxiv.org/abs/1806.04553