Quantum Random Number Generator with Internal Consistency Check and Public Verification

TL;DR

The paper tackles robustness and verifiability challenges in quantum random number generation by presenting a simple loop-based QRNG using passive optics, augmented with an internal consistency check based on the constant ratio $P_{l+1}/P_l \approx r(1-\eta)$ and a public verification channel that yields two disjoint streams, $S_{Q_1}$ and $S_{Q_2}$, with identical entropy. It provides a concrete experimental demonstration at $1310\,\text{nm}$ with $r=0.41$ and $\eta=0.230$, showing stable rate ratios and strong agreement with the theoretical model $p^l_{\text{click}} = 1 - e^{-\beta_l}$. The data support the dual-entropy property, as reflected by comparable non-iid entropy estimates for both sequences, enabling external auditing without compromising private randomness. Overall, the work demonstrates that robust, self-testing, and publicly verifiable quantum randomness can be achieved with a minimal optical footprint, beneficial for cryptographic and transparency-focused applications.

Abstract

Quantum Random Number Generators provide true physical randomness based on quantum processes, essential for cryptographic and scientific applications. However, practical implementations face challenges in robustness and verifiability: ensuring that the entropy source remains secure and stable over time, and enabling independent confirmation of randomness quality without compromising security. We present a system based on a simple looped beam splitter architecture that uses only passive optical components. The device features an intrinsic self-testing mechanism derived from the stability of detection-probability ratios, allowing continuous validation of correct operation. In addition, the same physical process generates two independent random sequences with identical entropy: a private sequence, used for secure applications, and a public one, enabling external statistical verification with zero mutual information between them. This approach demonstrates that robust, self-testing, and publicly verifiable quantum randomness can be achieved with minimal optical complexity without jeopardizing security.

Figures (6)

• Figure 1: Scheme of the loop-based QRNG. BS: Beam Splitter; M: Mirror; SPD: Single Photon Detector; $\eta$: effective system loss.
• Figure 2: Expected extractable bits per pulse $b(r;\eta,|\alpha|^2)$ versus reflectivity $r$ for several loss values $\eta$. Curves are obtained from $(P_1+P_2)\log_2\!\bigl((P_1+P_2)/P_1\bigr)$ with $P_l$ defined in the main text.
• Figure 3: Experimental setup of the QRNG device. A pulsed 1310 nm laser is attenuated and injected through a linear polarizer (LP) into a $40/60$ fiber beam splitter. The reflected output ($b_1$) is sent to a single-photon detector (SNSPD), while the transmitted output ($b_0$) is fed back to the other input port ($a_1$), forming a loop.
• Figure 4: Comparison between experimental detection probabilities and theoretical predictions using the measured parameters $r=0.41$ and $\eta=0.230$. The close agreement confirms that the experimental data follow the model described by Eq. (6).
• Figure 5: Detection rate ratios across different loop transits calculated over $0.6$-second intervals. The stability of the ratios confirms the constant relation $P_{l+1}/P_l \approx r(1-\eta)$ predicted by the model. Minor fluctuations in the third loop are attributed to lower detection statistics.