High-dimensional detection-loophole-free measurement-device-independent quantum random number generator

TL;DR

Cryptographic security hinges on private randomness, but device trust is challenging; fully device-independent QRNGs are impractical due to stringent requirements, motivating semi-device-independent and measurement-device-independent QRNGs. This work develops a high-dimensional MDI-QRNG using path-encoded weak coherent states and a cascaded fiber Sagnac interferometer network to implement tunable three-output beamsplitters, enabling real-time randomness certification with untrusted detectors. The experiment reports a certified randomness rate of 1.77 Mbps and up to 1.22 bits per round, surpassing the qubit benchmark of 0.92 bits and illustrating the benefits of higher-dimensional encoding. The results demonstrate a scalable, fiber-based platform suitable for practical QRNG deployment and motivate further exploration of higher-dimensional encodings and routed Bell self-testing for device independence.

Abstract

Certifying random number generators is challenging, especially in security-critical fields like cryptography. Here, we demonstrate a measurement-device-independent quantum random number generator (MDI-QRNG) using high-dimensional photonic path states. Our setup extends the standard qubit beam-splitter QRNG to a three-output version with tunable fiber-optic interferometers acting as tunable beam splitters and superconducting detectors. This setup generates over 1.2 bits per round and 1.77 Mbits per second of certifiably secure private randomness without requiring \emph{any} trust in the measurement apparatus, a critical requirement for the security of real-world cryptographic applications. Our results demonstrate certifiably secure high-dimensional quantum random-number generation, paving the way for practical, scalable QRNGs without the need for complex devices.

Figures (4)

• Figure 1: Experimental setup. A source of weak coherent states (WCS) prepares path-encoded qutrit states using two tunable beam splitters (TBSs). A function generator (FG) controls the intensity modulator (IM) used to chop the continuous-wave (CW) laser into 10 ns wide pulses, which are then attenuated to the single-photon level using a series of variable optical attenuators (ATT). The two tunable beamsplitters (TBSs) are each actually comprised of a fiber-optical Sagnac interferometer (inset), containing a phase modulator (PM) $\phi_x$, an optical fiber delay and manual polarization controllers (PC). The internal relative phase $\phi_x$ in each interferometer TBS controls the splitting ratio of the TBS. The three outputs of the TBSs are connected to three superconducting nanowire single-photon detectors (SNSPDs).
• Figure 2: Interference patterns of the first a) and second b) Sagnac interferometer as a function of the voltages applied to the phase modulators $\phi_1$ and $\phi_2$. Also highlighted are the settings that correspond to the test states $\ket{\psi_0}, \ket{\psi_1}$ and $\ket{\psi_2}$
• Figure 3: Experimental results of the qutrit QRNG. a) Certified bitrate over time. The certified bitrate is given by the detection rate (i.e. the symbol rate), multiplied with the amount of certified randomness per round. b) Success probability over time, of the test states, needed to provide randomness certification using the MDI protocol. Each point corresponds to one test state block, and they are not uniformly distributed since they are randomly chosen throughout the experiment (please see \ref{['sec:results']} and \ref{['appendix:methods-experimental-qutrit-mdi-qrng']}).
• Figure 4: Certified randomness per experimental round (data points) for the qutrit and qubit case, along with simulated certified randomness (line) for different mean photon numbers (see \ref{['appendix:methods-simulations']}). The experimental qubit (qutrit) cases achieves a maximum $0.92$ ($1.22$) certified bits/round at $\mu=0.91$ ($\mu=1.22$), taking into account the measured test state probabilities. This clearly demonstrates the advantage of employing higher-dimensional quantum states for certified randomness generation.