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

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.