Indistinguishability between quantum randomness and pseudo-randomness under efficiently calculable randomness measures

• URL: http://arxiv.org/abs/2309.11117v4
• Date: Tue, 16 Jan 2024 01:37:15 GMT
• Title: Indistinguishability between quantum randomness and pseudo-randomness under efficiently calculable randomness measures
• Authors: Toyohiro Tsurumaru, Tsubasa Ichikawa, Yosuke Takubo, Toshihiko Sasaki, Jaeha Lee, Izumi Tsutsui
• Abstract summary: We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudo-random numbers (i.e., random numbers generated algorithmically) The theorem states that one cannot distinguish these two types of random numbers if the quantum random numbers are efficiently classically simulatable and the randomness measure used for the distinction is efficiently computable.
• Score: 6.201566048090889
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudo-random numbers (i.e., random numbers generated algorithmically). The theorem states that one cannot distinguish these two types of random numbers if the quantum random numbers are efficiently classically simulatable and the randomness measure used for the distinction is efficiently computable. We derive this theorem by using the properties of cryptographic pseudo-random number generators, which are believed to exist in the field of cryptography. Our theorem is found to be consistent with the analyses on the actual data of quantum random numbers generated by the IBM Quantum and also those obtained in the Innsbruck experiment for the Bell test, where the degrees of randomness of these two set of quantum random numbers turn out to be essentially indistinguishable from those of the corresponding pseudo-random numbers. Previous observations on the algorithmic randomness of quantum random numbers are also discussed and reinterpreted in terms of our theorems and data analyses.

Related papers

• Generation of True Quantum Random Numbers with On-Demand Probability Distributions via Single-Photon Quantum Walks [5.201119608184586]
  We show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions. Our theoretical and experimental results exhibit high fidelity for various selected distributions.
  arXiv  Detail & Related papers  (2024-03-05T03:05:19Z)
• Pseudorandom Strings from Pseudorandom Quantum States [6.79244006793321]
  We study the relationship between notions of pseudorandomness in the quantum and classical worlds. We show that a natural variant of pseudorandom generators called quantum pseudorandom generators (QPRGs) can be based on the existence of logarithmic output length PRSGs. We also study the relationship between other notions, namely, pseudorandom function-like state generators and pseudorandom functions.
  arXiv  Detail & Related papers  (2023-06-09T01:16:58Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Testing randomness of series generated in Bell's experiment [62.997667081978825]
  We use a toy fiber optic based setup to generate binary series, and evaluate their level of randomness according to Ville principle. Series are tested with a battery of standard statistical indicators, Hurst, Kolmogorov complexity, minimum entropy, Takensarity dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin to check station exponent. The level of randomness of series obtained by applying Toeplitz extractor to rejected series is found to be indistinguishable from the level of non-rejected raw ones.
  arXiv  Detail & Related papers  (2022-08-31T17:39:29Z)
• On the effects of biased quantum random numbers on the initialization of artificial neural networks [3.0736361776703562]
  A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness. Recent results suggest that benefits can indeed be achieved from the use of quantum random numbers.
  arXiv  Detail & Related papers  (2021-08-30T15:50:07Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Single photon randomness originating from the symmetry of dipole emission and the unpredictability of spontaneous emission [55.41644538483948]
  Quantum random number generation is a key ingredient for quantum cryptography and fundamental quantum optics. We experimentally demonstrate quantum random number generation based on the spontaneous emission process. The scheme can be extended to random number generation by coherent single photons with potential applications in solid-state based quantum communication at room temperature.
  arXiv  Detail & Related papers  (2021-02-18T14:07:20Z)
• Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators [0.0]
  Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences. We present the results of a search for algorithmic randomness and incomputability in the output from two different QRNGs.
  arXiv  Detail & Related papers  (2021-01-04T21:17:34Z)
• The Effects of Quantum Randomness on a System Exhibiting Computational Creativity [0.0]
  We present experimental results on the effects of using quantum or 'truly' random numbers, as opposed to pseudorandom numbers, in a system that exhibits computational creativity. The results indicate that using quantum random numbers too often or too seldom in the composing process does not have any positive effect on the output generated. There is a'sweet spot' of using quantum random numbers 15% of the time that results in fewer statistical outliers.
  arXiv  Detail & Related papers  (2020-08-22T04:34:17Z)
• Quantum Random Number Generation using a Solid-State Single-Photon Source [89.24951036534168]
  Quantum random number generation (QRNG) harnesses the intrinsic randomness of quantum mechanical phenomena. We demonstrate QRNG with a quantum emitter in hexagonal boron nitride. Our results open a new avenue to the fabrication of on-chip deterministic random number generators.
  arXiv  Detail & Related papers  (2020-01-28T22:47:43Z)
• Using Randomness to decide among Locality, Realism and Ergodicity [91.3755431537592]
  An experiment is proposed to find out, or at least to get an indication about, which one is false. The results of such experiment would be important not only to the foundations of Quantum Mechanics.
  arXiv  Detail & Related papers  (2020-01-06T19:26:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.