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Quantum True Random Number Generation via Schmidt-Mode-Filtered SPDC with Finite-Size Security Constraints

Tawfik Ismail, Ala H. Sabeeh

Published Jul 30, 2025• 0 citations
Publisher

Abstract

Abstract This work proposes a quantum true random number generator (QTRNG) architecture based on spontaneous parametric down-conversion (SPDC) photon sources, single-photon avalanche diodes (SPADs), and Schmidt-mode-resolved joint spectral intensity (JSI) filtering. The system employs a numerically optimized spectral filter to isolate the dominant Schmidt mode, effectively suppressing spectral entanglement and enhancing source-level purity. Simulation results confirm that the optimized configuration achieves a Schmidt number of $1.0008$, spectral purity of $0.9992$, and entanglement entropy of $0.0052$ bits. The bitstream generated from coincidence detections demonstrates ideal statistical properties, including a min-entropy per bit of $H_\infty = 0.9997$ and a total of $17.85$ million extractable bits, without requiring post-processing. The randomness output passes all tests in the NIST SP 800-22 and Dieharder suites with a $100\%$ success rate, confirming its unpredictability and cryptographic suitability. The system is also computationally efficient, with a runtime of $320$ seconds and memory usage of $12.83$~MB for $10^9$ pulses, making it suitable for real-time embedded applications. This study establishes a scalable and physically secure QTRNG framework grounded in spectral mode engineering and finite-size security certification.

DOI
10.21203/rs.3.rs-7041346/v1

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Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth ≈\approx≈ 5.23 GHzGHzGHz) operated near threshold and a $\sim$48 cmcmcm fiber delay line, a raw data generation rate of 2.0 GbpsGbpsGbps is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 GbpsGbpsGbps in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.
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