Semi-Device-Independent Quantum Random Number Generator Resistant to General Attacks

TL;DR

This work tackles secure quantum random number generation under general, non-i.i.d. attacks within a semi-device-independent framework by imposing an energy-bound constraint on emitted quantum states and employing a continuous-variable, heterodyne-based scheme with three ternary inputs. The protocol proceeds in three steps—preparations and measurements, quantum entropy estimation, and randomness extraction—and uses a semidefinite program to bound Eve's guessing probability, complemented by Kato's inequality to account for finite-size effects. Experimentally, the authors demonstrate the scheme on a CV fiber system with off-the-shelf components, achieving a net randomness rate of $R_{\text{net}} \approx 0.01165$ bits per round (1.165 Mbps at 100 MHz) while ensuring the output passes standard randomness tests. The approach delivers a practical, robust semi-DI QRNG that tolerates general attacks, reduces device characterization demands, and enables high-throughput secure random number generation for cryptographic and computational applications.

Abstract

Quantum random number generators (QRNGs) produce true random numbers based on the inherent randomness of quantum theory, rendering them a foundational segment of quantum cryptography. Distinguished from trusted-device QRNGs whose security depends on characterized devices, semi-device-independent (semi-DI) QRNGs permit partial devices to be defective or even maliciously manipulated, which achieves a good trade-off between generation rate and security. In this paper, we propose a semi-DI QRNG that resists general attacks while accounting for finite-size effects. The protocol requires no rigorous characterization of the source and measurement devices other than limiting the energy of the emitted states, significantly reducing the demands on practical QRNG systems. Leveraging the tight Kato inequality for correlated variables, we show that our protocol generates more randomness than it consumes. Furthermore, we demonstrate the scheme on a continuous-variable system with ternary inputs of states. Heterodyne detection is employed to enable phase compensation through data postprocessing, alleviating the stringent requirement on system stability. The system operates at 100 MHz, achieving a net random number generation rate of 1.165 Mbps at 5.3x10^9 rounds. Our work offers a promising approach to achieve both the robust security and high generation rate with a simple experimental setup.

Figures (6)

• Figure 1: (a) Schematic diagram of the complementary modulation and measurement. The modulated quantum states have the same intensity $\mu$ but different phases. In each QRNG execution round, two successive temporal modes of coherent states are modulated with a $\pi$ phase difference. The early mode ($\rho_1, \rho_2$ or $\rho_3$ ) serves as the prepared state in the protocol, while the corresponding late mode ($\rho_1', \rho_2'$ or $\rho_3'$ ) acts as an auxiliary state to balance the DC level of the homodyne detectors. The measured results of the two quadratures $(X,P)$ are discretized into $D_1$, $D_2$, $D_3$ and $D_4$. (b) Impact of phase drifts on observed states in phase space, where the prepared states undergo a random rotation over time.
• Figure 2: (a) Simulations of the net randomness generation rate versus the probability of test rounds, with $\mu = 0.005$, $\eta=23.2\%$, $N=5.3\times10^9$ and $\epsilon = 10^{-10}$. (b) Simulations of the net randomness generation rate versus detection efficiency for different total number of rounds, with $\epsilon = 10^{-10}$, optimized mean photon number and probability of test rounds.
• Figure 3: Experimental setup of the Semi-DI QRNG. The phase of the input signal is randomly modulated by a PM, while its amplitude is evaluated through the Meter reading from the trusted part. After optimizing the intensity of LO, the prepared state is interfered with the LO in a 90° OH, followed by measurement of two quadratures using a pair of BDs. Through the statistical dependence between the prepared states and measurement outcomes, the lower bound on the generated randomness is established. BS: beam splitter; VOA: variable optical attenuator; Meter: optical power meter; PM: phase modulator; ATT: fixed optical attenuator; 90° OH: 90° optical hybrid; BD: balanced amplified photodetector; AWG: arbitrary waveform generator; MSO: mixed-signal oscilloscope.
• Figure 4: Data frame configuration of QRNG experiment. Reference signals for data synchronization are periodically inserted between the valid signals used for QRNG execution. The valid signals consist of the prepared and auxiliary signals required for the complementary modulation.
• Figure 5: Phase drift of the prepared state $\rho_3$ versus time. The phase is evaluated at intervals of $2\,\mathrm{ms}$.