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arXiv:2301.11973

Gain-switched VCSEL as a quantum entropy source: the problem of quantum and classical noise

Roman Shakhovoy, Elizaveta Maksimova

Published Jan 1, 2022• 5 citations
arXivHTMLPDF

Abstract

We consider the problem of quantum noise extraction from polarization swapping in a gain-switched VCSEL. The principle of operation of a quantum random number generator is based on the generation of laser pulses with one of two orthogonal polarization states, followed by digitization of polarization-resolved pulses with a comparator. At intensity values of laser pulses close to the threshold value of the comparator, the contribution of the classical noise of the photodetector will have a crucial role in making a decision on the choice of a logical zero or one. We show how to evaluate the contribution of classical noise and how to calculate the quantum reduction factor required for post-processing.

DOI
10.18721/jpm.153.237

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We consider the problem of quantum noise extraction from polarization swapping in a gain-switched VCSEL. The principle of operation of a quantum random number generator is based on the generation of laser pulses with one of two orthogonal polarization states, followed by digitization of polarization-resolved pulses with a comparator. At intensity values of laser pulses close to the threshold value of the comparator, the contribution of the classical noise of the photodetector will have a crucial role in making a decision on the choice of a logical zero or one. We show how to evaluate the contribution of classical noise and how to calculate the quantum reduction factor required for post-processing.
We experimentally study a quantum random number generator based on the random excitation of the linearly polarized modes of a gain-switched vertical-cavity surface-emitting laser (VCSEL). Our device is characterized by having polarization switching under continuous wave operation. By measuring the linear polarization mode that is excited in each pulse we collect a sufficient number of bits to evaluate if a standard statistical test suite is passed. We consider linear and Von Neumann post-processing methods in order to reduce the bias with different levels of bits rejection. The post-processed bit strings pass all tests in the standard test suite for random number generators provided by the National Institute of Standards and Technology (NIST). We finally compare the results obtained with different post-processing functions, including several [ n , k , d ] linear BCH codes. We show that large values of n and k are the best choice to obtain simultaneously improved throughput and randomness.
Abstract Random number generators (RNGs) are an essential ingredient of modern cryptographic systems. Particular attention is paid today to a special class of RNGs – quantum RNGs, which are attracting close attention of researchers due to the explosive development of quantum key distribution systems, where the use of quantum randomness is a necessary security requirement. A large number of various quantum entropy sources have been proposed over the last 10-15 years. Most of them are based on the use of different quantum optics phenomena, particularly, on the effects occurring in semiconductor lasers. This choice is due to the relatively low cost and ease of use of such devices and the high random bit generation rate available with optical QRNGs. Motivated by these reasons, we study in the present research the QRNG based on variations of light polarization in a vertical-cavity surface-emitting laser (VCSEL). The scheme we propose allows creating an extremely compact and fast optical QRNG, consisting essentially of only a laser and a polarizing beam splitter. We revealed that it is possible to ensure the pulsed operation of a VCSEL in a bistable regime, which is characterized by random switch of light polarization. We show, however, that probabilistic properties of such laser pulses significantly depend on the internal laser parameters as well as on its operating mode. Understanding these properties is fundamentally important for the correct assessment of the quantum noise contribution and, consequently, for the subsequent post-processing of digitized random sequences.
We have experimentally demonstrated that the random excitation of the linear orthogonal polarization modes of a gain-switched vertical-cavity surface-emitting laser (VCSEL) can be used for quantum random number generation. Our VCSEL presents polarization switching under continuous wave operation. Adjusting the modulation conditions and sampling times, both polarization modes of the VCSEL can be excited with equal probability. Random bits are obtained comparing the two orthogonal polarized signals at a sampling time. The random bits obtained pass some of the National Institute of Standards and Technology (NIST) statistical tests.
Semiconductor lasers are normally used as single-photon sources in most commercial and research quantum key distribution (QKD) systems [1]. These lasers are also used for quantum random number generation (QRNG) that is a necessary security requirement for QKD. In device-dependent QRNGs unpredictability is guaranteed by comparing experimental measurements with simulation data obtained from a model of the physical entropy source [2]. The characterization of phase fluctuations in a gain-switched edge-emitting semiconductor laser for QRNG has been recently performed [2]. Very recently a QRNG based on the random excitation of the linearly polarized modes of a gain-switched vertical-cavity surface-emitting laser (VCSEL) has also been proposed [3]. In this work we characterize the polarization fluctuations found in this system by comparing experimental measurements with the results obtained from the simulation of a VCSEL's model that incorporates the device intrinsic parameters found using state-of-the-art experimental techniques [4].
In the study of quantum random number generators (QRNGs), the problem of random signal digitization is often not considered in detail. However, in the context of a standalone QRNG device, this issue is very important. In this paper, we consider the problem of digitizing laser pulses with random intensity and analyze various approaches used to estimate the contribution of classical noise. A simple method for determining the quantum reduction factor suitable for digitization with an analog-to-digital converter is proposed.
Gain-switched lasers are in demand in numerous quantum applications, particularly in systems of quantum key distribution and in various optical quantum random number generators. The reason for this popularity is natural phase randomization between gain-switched laser pulses. The idea of such randomization has become so familiar that most authors use it without regard to the features of the laser operation mode they use. However, at high repetition rates of laser pulses or when pulses are generated at a bias current close to the threshold, the phase randomization condition may be violated. This paper describes theoretical and experimental methods for estimating the degree of phase randomization in a gain-switched laser. We consider in detail different situations of laser pulse interference and show that the interference signal remains quantum in nature even in the presence of classical phase drift in the interferometer provided that the phase diffusion in a laser is efficient enough. Moreover, we formulate the relationship between the previously introduced quantum reduction factor and the leftover hash lemma. Using this relationship, we develop a method to estimate the quantum noise contribution to the interference signal in the presence of phase correlations. Finally, we introduce a simple experimental method based on the analysis of statistical interference fringes, providing more detailed information about the probabilistic properties of laser pulse interference.