Optimization of experimental quantum randomness expansion

TL;DR

This work addresses quantifying and maximizing randomness generated by a device-independent QRNG based on Bell violations. It employs the Entropy Accumulation Theorem with a min-trade-off function, optimizing the smoothing parameter $ε_{ ext{s}}$, test-round probability $γ$, and non-aborting probability $p_ extOmega$, while accounting for switching delays. Through experimental SPDC-based entanglement, and computational benchmarking with the NPA and Brown-Fawzi-Fawzi frameworks, it shows CHSH can reach high asymptotic rates at $7.0 imes10^4$ events/s, and a carefully chosen $ε_{ ext{s}}$ and generation time yield net rates exceeding 50 kbps for long chunks, outperforming previous implementations. The study provides practical guidelines for QRNG design, balancing randomness quality, generation rate, and robustness to finite-size effects and hardware delays, with potential extensions to alternative Bell expressions and faster switching. The results demonstrate a significant step toward high-rate, secure quantum randomness generation suitable for cryptographic applications, under realistic experimental constraints.

Abstract

Quantum technologies provide many applications for information processing tasks that are impossible to realize within classical physics. These capabilities include such fundamental resources as generating secure, i.e. private and unpredictable random values. Yet, the problem of quantifying the amount of generated randomness is still not fully solved. This work presents a comprehensive analysis of the design and performance optimization of a Quantum Random Number Generator (QRNG) based on Bell inequality violations. We investigate key protocol parameters, including the smoothing parameter ($ε_{\text{s}}$), test round probability ($γ$), and switching delays, and their effects on the generation rate and quality of randomness. We identify optimal ranges for $γ$ and $p_Ω$ (the protocol's non-aborting probability) to balance the trade-off between randomness consumption and net randomness generation. Additionally, we explore the impact of switching delays on the system's performance, providing strategies to mitigate these effects. Our results indicate substantial developments in QRNG implementations and offer higher randomness expansion rates. The work provides practical guidelines for the efficient and secure design of QRNG systems and other cryptographic protocols.

Figures (7)

• Figure 1: (Color online) Experimental setup. Entangled photon pairs are generated through the SPDC process. The emitted photons in modes (a) and (b) are coupled to single-mode fiber (SMF) and pass narrow filters (F). Each of the two stations’ measurements is composed of a half-wave plate (HWP), a polarization beam splitter (PBS), and single photon detectors ($D_{+}$ and $D_{-}$). (See main text for details).
• Figure 2: (Color online) The net generation rate for 70,000 events per second using the Bell inequality CHSH, with the smoothing parameter $\epsilon_{\text{s}} = 1 \times 10^{-15}$, depends significantly on the generation time for each data chunk. The minimum generation time required to achieve a positive rate is 6 minutes. The range of generation times explored extends up to 24 hours. It is important to note that the asymptotic generation rate reported in Table \ref{['tab:prop2_Bell']} exceeds the values shown in the plot. This suggests that increasing the generation time can further mitigate the impact of finite data size effects, thereby enhancing the certified randomness rate. The data point at 69,120 seconds (19.2 hours) was specifically chosen to compare with the results presented in liu2021device, where this value was utilized.
• Figure 3: (Color online) Effect of the test round probability $\gamma$ and the protocol non-aborting probability $p_\Omega$ on the generation rate, for a single data chunk generation time of 10 minutes. This analysis assumes the smoothing parameter $\epsilon_{\text{s}} = 1 \times 10^{-15}$ and uses the Bell inequality CHSH at an event rate of 70,000 per second.
• Figure 4: (Color online) Impact of the test round probability $\gamma$ and the protocol's non-aborting probability $p_\Omega$ on the generation rate, with a single data chunk generation time of 1 hour. The protocol parameters are consistent with those used in Figure \ref{['fig:gammaandpomega10minutes']}.
• Figure 5: (Color online) The expansion rate, defined as the ratio of total net randomness generated to the total randomness consumed, for single data chunk generation times of 10 minutes and 1 hour. The analysis considers the smoothing parameter $\epsilon_{\text{s}} = 1 \times 10^{-15}$ and employs the Bell inequality CHSH with an event rate of 70,000 per second.