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arXiv:2604.12724

Testing the 3D QRNG by Undoing

J. M. Agüero Trejo, Cristian S. Calude, O. C. Stoica

quant-phSubmitted Apr 14, 2026• Announced Apr 15, 2026• 0 citations
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Abstract

We propose a method to test whether a photonic 3D QRNG works according to the underlying theory, thereby generating highly incomputable/unpredictable sequences of random digits. The test relies on undoing the unitary evolution realized by the 3D QRNG. The test verifies the unitarity, the magnitude of the noise, and other potential errors, such as photon loss or systematic and reproducible fabrication errors. Therefore, the test can confirm the theoretically proven features of the 3D QRNG, such as strong incomputability and unpredictability, or how one has to correct it, if necessary. In addition, the test ensures that the QRNG is not affected by limits of quantum measurement accuracy, as those described in the Wigner-Araki-Yanase Theorem. The test can be easily incorporated into the QRNG and used as a means of experimental certification.

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11 pages, 6 figures

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We propose a method to test whether a photonic 3D QRNG works according to the underlying theory, thereby generating highly incomputable/unpredictable sequences of random digits. The test relies on undoing the unitary evolution realized by the 3D QRNG. The test verifies the unitarity, the magnitude of the noise, and other potential errors, such as photon loss or systematic and reproducible fabrication errors. Therefore, the test can confirm the theoretically proven features of the 3D QRNG, such as strong incomputability and unpredictability, or how one has to correct it, if necessary. In addition, the test ensures that the QRNG is not affected by limits of quantum measurement accuracy, as those described in the Wigner-Araki-Yanase Theorem. The test can be easily incorporated into the QRNG and used as a means of experimental certification.
We construct a class of three-dimensional photonic quantum random number generators (QRNGs) and prove that each of them generates maximally unpredictable digits via measurements that are robust to errors. This shows that every sequence generated is strongly incomputable; hence its quality is provably better than that of every pseudo-random sequence. These results suggest that incomputability in physics is real and practically applicable. Finally, we present photonic implementations of three-dimensional QRNGs and discuss device independence.
Standard pseudo-random generators have weaknesses that have led to the development of quantum random number generators (QRNGs). However, common QRNG validation methods, whether based on quantum indeterminism or statistical tests, are insufficient to guarantee high-quality randomness. In contrast, a mathematical theory based on the Located Kochen-Specker Theorem proves that 3D QRNGs produce maximally unpredictable outputs without using entanglement, and both theory and experiments have supported their security. The paper focuses on a practical photonic implementation of a 3D QRNG that is easier to deploy than cryogenic superconducting implementations. As any physical implementation is subject to various measurement errors, it is important to study theoretically and experimentally the type and role of errors in 3D QRNGs. In this paper, we will model the photonic 3D QRNG as an open quantum system, constructed as an arrangement of imperfect beam-splitters with a range of losses based on the fidelity of its components, and we will show that under certain conditions, the process remains within the scope of the Kochen-Specker Theorem, which guarantees maximum unpredictability.
In this paper we propose a quantum random number generator (QRNG) that uses an entangled photon pair in a Bell singlet state and is certified explicitly by value indefiniteness. While ‘true randomness’ is a mathematical impossibility, the certification by value indefiniteness ensures that the quantum random bits are incomputable in the strongest sense. This is the first QRNG setup in which a physical principle (Kochen–Specker value indefiniteness) guarantees that no single quantum bit that is produced can be classically computed (reproduced and validated), which is the mathematical form of bitwise physical unpredictability. We discuss the effects of various experimental imperfections in detail: in particular, those related to detector efficiencies, context alignment and temporal correlations between bits. The analysis is very relevant for the construction of any QRNG based on beam-splitters. By measuring the two entangled photons in maximally misaligned contexts and using the fact that two bitstrings, rather than just one, are obtained, more efficient and robust unbiasing techniques can be applied. We propose a robust and efficient procedure based onXORing the bitstrings together – essentially using one as a one-time-pad for the other – to extract random bits in the presence of experimental imperfections, as well as a more efficient modification of the von Neumann procedure for the same task. We also discuss some open problems.
Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.
In this Thesis, we develop the only class of QRNGs, to date, that has been proved to be better than any PRNG. This type of QRNG is based on a located form of the Kochen-Specker Theorem. This certification is unique because i) the assumptions used have been experimentally validated, ii) the robustness of measurements was proved theoretically, iii) the quality of quantum random digits generated with this class of QRNG was experimentally shown to be better than that of the best PRNGs, demonstrating for the first time the strong effects of incomputability on the outputs of a quantum random number generator. Finally, we propose a method using high-quality randomness for inverting a class of one-way functions in a pre-given time.
Abstract 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.