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Register a new userExperimental Evidence of Quantum Randomness Incomputability
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In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e. it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic property --- of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
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The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudo-random sequences are necessarily computable, a highly nontypical property of sequences. In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen-Specker Theorem, to see whether such evidence can be found in practice. While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and incomputability is a nontrivial task. We present the results of a search for algorithmic randomness and incomputability in the output from two different QRNGs, performed by applying tests based on the Solovay-Strassen test of primality and the Chaitin-Schwartz theorem. The first QRNG uses measurements of quantum vacuum fluctuations. The second QRNG is based on polarization measurements on entangled single photons; for this generator, we use looped (and thus highly compressible) strings that also allow us to assess the ability of the tests to detect repeated bit patterns. Compared to a previous search for algorithmic randomness, our study increases statistical power by almost 3 orders of magnitude.
Coherently manipulating multipartite quantum correlations leads to remarkable advantages in quantum information processing. A fundamental question is whether such quantum advantages persist only by exploiting multipartite correlations, such as entanglement. Recently, Dale, Jennings, and Rudolph negated the question by showing that a randomness processing, quantum Bernoulli factory, using quantum coherence, is strictly more powerful than the one with classical mechanics. In this Letter, focusing on the same scenario, we propose a theoretical protocol that is classically impossible but can be implemented solely using quantum coherence without entanglement. We demonstrate the protocol by exploiting the high-fidelity quantum state preparation and measurement with a superconducting qubit in the circuit quantum electrodynamics architecture and a nearly quantum-limited parametric amplifier. Our experiment shows the advantage of using quantum coherence of a single qubit for information processing even when multipartite correlation is not present.
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 $5.47times10^8$ quantum-proof random bits while consuming $4.39times10^8$ bits of entropy, expanding our store of randomness by $1.08times10^8$ bits at a latency of about $13.1$ h, with a total soundness error $4.6times10^{-10}$. 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.
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 a certified error bounded by $2^{-64}approx 5.42times 10^{-20}$.
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