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arXiv:2608.24729

Cosmic muon arrival directions as a source of entropy

Deepak Samuel

Published Sep 18, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract We demonstrate, for the first time, that the arrival directions of cosmic-ray muons from a muon telescope provide a measurable source of physical entropy. Using six months of data collected from a muon telescope, the local zenith and azimuth angles were used for randomness extraction. The result of this study show that each cosmic muon track from our detector can generate upto 4 bits with an entropy of 0.999182 bits/bit with a maximum bit rate of roughly 650 bits/s which can possibly be enhanced by improving the detector size and angular resolution. The suggested technique can be potentially used as a random number generator required for closing the settings-independence loophole in the tests for violations of Bell's inequality. The data acquisition, data reduction, and conditioning algorithms are discussed in detail.

DOI
10.21203/rs.3.rs-10949036/v1

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Abstract We demonstrate, for the first time, that the arrival directions of cosmic-ray muons from a muon telescope provide a measurable source of physical entropy. Using six months of data collected from a muon telescope, the local zenith and azimuth angles were used for randomness extraction. The result of this study show that each cosmic muon track from our detector can generate upto 4 bits with an entropy of 0.999182 bits/bit with a maximum bit rate of roughly 650 bits/s which can possibly be enhanced by improving the detector size and angular resolution. The suggested technique can be potentially used as a random number generator required for closing the settings-independence loophole in the tests for violations of Bell's inequality. The data acquisition, data reduction, and conditioning algorithms are discussed in detail.
Privacy and security require not only strong algorithms but also reliable and readily available sources of randomness. To tackle this problem, one of the causes of single-event upsets is the utilization of a non-deterministic entropy source, specifically ultra-high energy cosmic rays. An adapted prototype based on existing muon detection technology was used as the methodology during the experiment and tested for its statistical strength. Our results show that the random bit sequence extracted from the detections successfully passed established randomness tests. The detections correspond to cosmic rays recorded using a common smartphone during our experiment. Despite the limited sample, our work provides valuable insights into the use of ultra-high energy cosmic rays as an entropy source.
True Random Number Generators (TRNGs) are the cornerstone of modern cryptographic applications. In this work, we present the first quantum1random number generator based on muon detection. The proposed implementation utilizes silicon photomultipliers and plastic scintillators to convert the time interval between crossing muons to random bits. Compared to the state-of-the-art, this design operates using a passive entropy source, scaling down its power consumption significantly. Additionally, the proposed muon-based TRNG can be fully integrated in modern computer hardware, making it suitable for low-power embedded device applications. We evaluate the proposal on its throughput and ability to pass standard randomness tests. Our method is successful in passing the NIST STS SP 800-22 and Dieharder evaluations. Finally, the implementation is compared to other well-established methods of generating random numbers.1We use the term “quantum” to denote the utilization of elementary particles as the output generation source, and not necessarily their properties, similar to related work [1], [2].
We propose a practical scheme to use photons from causally disconnected cosmic sources to set the detectors in an experimental test of Bell's inequality. In current experiments, with settings determined by quantum random number generators, only a small amount of correlation between detector settings and local hidden variables, established less than a millisecond before each experiment, would suffice to mimic the predictions of quantum mechanics. By setting the detectors using pairs of quasars or patches of the cosmic microwave background, observed violations of Bell's inequality would require any such coordination to have existed for billions of years-an improvement of 20 orders of magnitude.
Photons from distant astronomical sources can be used as a classical source of randomness to improve fundamental tests of quantum nonlocality, wave-particle duality, and local realism through Bell's inequality and delayed-choice quantum eraser tests inspired by Wheeler's cosmic-scale Mach-Zehnder interferometer gedanken experiment.Such sources of random numbers may also be useful for information-theoretic applications such as key distribution for quantum cryptography.Building on the design of an astronomical random number generator developed for the recent cosmic Bell experiment [Handsteiner et al.Phys. Rev. Lett. 118, 060401 (2017)], in this paper we report on the design and characterization of a device that, with 20-nanosecond latency, outputs a bit based on whether the wavelength of an incoming photon is greater than or less than ≈700 nm.Using the one-meter telescope at the Jet Propulsion Laboratory Table Mountain Observatory, we generated random bits from astronomical photons in both color channels from 50 stars of varying color and magnitude, and from 12 quasars with redshifts up to z = 3.9.With stars, we achieved bit rates of ∼1 × 10 6 Hz/m 2 , limited by saturation of our single-photon detectors, and with quasars of magnitudes between 12.9 and 16, we achieved rates between ∼10 2 and 2 × 10 3 Hz/m 2 .For bright quasars, the resulting bitstreams exhibit sufficiently low amounts of statistical predictability as quantified by the mutual information.In addition, a sufficiently high fraction of bits generated are of true astronomical origin in order to address both the locality and freedom-of-choice loopholes when used to set the measurement settings in a test of the Bell-CHSH inequality.
Random numbers are indispensable for a variety of applications ranging from testing physics foundations to information encryption. In particular, nonlocality test provide strong evidence for our current understanding of nature-quantum mechanics. All the random number generators (RNGs) used for the existing tests are constructed locally, making the test results vulnerable to the freedom-of-choice loophole. We report an experimental realization of RNGs based on the arrival time of cosmic photons. The measurement outcomes (raw data) pass the standard NIST statistical test suite. We present a realistic design to employ these RNGs in a Bell test experiment, which addresses the freedom-of-choice loophole.
Quantum random number generators (QRNGs) are an integral part of quantum key distribution (QKD) systems. To better understand the inherent physical processes, we compare the random numbers generated by two separate schemes, one is based on entropy (arrival time of photons) and another with an additional source of entropy (space) i.e, path superposition of arrival time of photons from a weak coherent source on a gated InGaAs single photon detector. Both experiments yield bits that appear random. However, they satisfy different criteria of randomness. The weak coherent source has a Poissonian distribution and extracting the variation about the arrival time of photons on gated SPD yields a source of random numbers that pass most of the Dieharder Tests. With the inclusion of superposition, we obtain random numbers that pass all the Dieharder tests. The physical origins of the random numbers in the two experiments is different, one is single entropy source based and other one is two entropy source based, and this is reflected in the outcomes of the different tests for randomness.