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arXiv:2607.11806

Phase synchronization dynamics of two mutually coupled InP lasers in a quantum entropy source

Berta Martínez-Pàmias, Miquel Rudé, Cristina Masoller

Published Jul 13, 2026• 0 citations
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Abstract

Quantum random number generators, at the core of digital trust infrastructures, rely on quantum entropy sources (QESs) to produce randomness from physical processes. The quantum origin certification of a QES requires a physical model compatible with the measured signal of the device. Here, we study Quside Technologies' phase-diffusion QES consisting of a photonic integrated circuit (PIC) that uses the interference of two indium phosphide (InP) lasers operated in gain-switching by simultaneously modulating their pump currents from below to above the threshold. This produces intensity pulses in each laser that have random optical phases due to quantum spontaneous emission. The lasers' intensities interfere via heterodyning, and from the interference signal a random bit is obtained per modulation cycle. While this system offers high scalability and compactness, residual coupling between the two lasers can induce phase synchronization, thus reducing its extractable entropy. Through experiments and simulations of a physical model based on coupled stochastic rate equations, we quantify this effect and link laser coupling to phase synchronization. We further derive an analytical model for the probability distribution of the measured interference intensity, enabling direct extraction of the quantum phase difference distribution and laying the groundwork for the QES optimization.

DOI
10.48550/arxiv.2607.11806

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Quantum random number generators, at the core of digital trust infrastructures, rely on quantum entropy sources (QESs) to produce randomness from physical processes. The quantum origin certification of a QES requires a physical model compatible with the measured signal of the device. Here, we study Quside Technologies' phase-diffusion QES consisting of a photonic integrated circuit (PIC) that uses the interference of two indium phosphide (InP) lasers operated in gain-switching by simultaneously modulating their pump currents from below to above the threshold. This produces intensity pulses in each laser that have random optical phases due to quantum spontaneous emission. The lasers' intensities interfere via heterodyning, and from the interference signal a random bit is obtained per modulation cycle. While this system offers high scalability and compactness, residual coupling between the two lasers can induce phase synchronization, thus reducing its extractable entropy. Through experiments and simulations of a physical model based on coupled stochastic rate equations, we quantify this effect and link laser coupling to phase synchronization. We further derive an analytical model for the probability distribution of the measured interference intensity, enabling direct extraction of the quantum phase difference distribution and laying the groundwork for the QES optimization.
We present an experimental and numerical study of the probability distribution of interference pulses from two InP lasers in a photonic integrated circuit (PIC) operated in gain-switching mode through a square-wave signal that turns them on and off. Without laser coupling, the lasers’ phases are random due to quantum spontaneous emission noise, and their phase difference can be translated into a random intensity and exploited for quantum random number generation (QRNG). We analyze the coupling dynamics that lead to optical phase synchronization. Through a direct comparison between experiments and simulations, we demonstrate a clear correlation between laser coupling and the degradation of the randomness of the lasers’ optical phases, providing a better understanding of the operation and performance of the QRNG device.
We performed an experimental and numerical study of an Indium Phosphide (InP) photonic integrated circuit (PIC) designed for quantum random number generation. We studied the dynamics of two weakly mutually coupled semiconductor lasers, and the transient evolution towards the synchronization of the lasers’ optical phases. By carefully adjusting the parameters of a rate-equation model, the simulated dynamics was found to be in qualitatively good agreement with the experimentally observed time traces. Our results allow us to better understand the transient evolution towards synchronization, and provide a foundation for the optimization of the system for photonic quantum random number generation.
We performed an experimental and numerical study of an Indium Phosphide photonic integrated circuit designed for quantum random number generation. We investigated the dynamics of two weakly mutually coupled semiconductor lasers and the transient evolution towards the synchronization of the lasers’ optical phases. The simulated dynamics with the experimentally adjusted parameters were found to be in qualitatively good agreement with the experimental time traces. The results provide a better understanding of the evolution towards synchronization and a foundation for the optimization of the photonic quantum random number generation system.
Random number generators are essential to ensure performance in information technologies, including cryptography, stochastic simulations and massive data processing.The quality of random numbers ultimately determines the security and privacy that can be achieved, while the speed at which they can be generated poses limits to the utilisation of the available resources.In this work we propose and demonstrate a quantum entropy source for random number generation on an indium phosphide photonic integrated circuit made possible by a new design using two-laser interference and heterodyne detection.The resulting device offers high-speed operation with unprecedented security guarantees and reduced form factor.It is also compatible with complementary metal-oxide semiconductor technology, opening the path to its integration in computation and communication electronic cards, which is particularly relevant for the intensive migration of information processing and storage tasks from local premises to cloud data centres.
We performed an experimental and numerical study of an Indium Phosphide photonic integrated circuit designed for quantum random number generation. We investigated the dynamics of two weakly mutually coupled semiconductor lasers and the transient evolution towards the synchronization of the lasers’ optical phases. The simulated dynamics with the experimentally adjusted parameters were found to be in qualitatively good agreement with the experimental time traces. The results provide a better understanding of the evolution towards synchronization and a foundation for the optimization of the photonic quantum random number generation system.
Quantum random number generation (QRNG) has become a topic of growing interest in recent years due to important applications in cryptography and simulations. Interferometric detection of phase diffusion in gain-switched single-mode semiconductor lasers is one of the main generation techniques. In this paper, we study experimentally and theoretically the phase diffusion in gain-switched discrete mode laser diodes. We derive a stochastic rate equations model for the laser electric field that avoids numerical instabilities that appear when simulating amplitude and phase equations. Measurements are performed in order to extract the parameters of our semiconductor laser. Spontaneous emission rate coupled into the lasing mode is measured as a function of the carrier number for bias currents below threshold. A quadratic dependence is obtained that permits us to evaluate the validity of the linear approximations that have been used to describe laser phase diffusion in QRNG. The good agreement between experiments and theory permits us to give a realistic quantitative description of the dynamical evolution of the phase statistics in this type of QRNGs.