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Optics Letters

High-speed quantum random number generation by measuring phase noise of a single-mode laser

Bing Qi, Yue-Meng Chi, Hoi‐Kwong Lo, Li Qian

Published Jan 21, 2010• 289 citations
Publisher

Abstract

We present a high-speed random number generation scheme based on measuring the quantum phase noise of a single-mode laser operating at a low intensity level near the lasing threshold. A delayed self-heterodyning system has been developed to measure the random phase fluctuation. By actively stabilizing the phase of the interferometer, a random number generation rate of 500 Mbit/s has been demonstrated and the generated random numbers have passed all the DIEHARD tests.

DOI
10.1364/ol.35.000312

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We present a high-speed random number generation scheme based on measuring the quantum phase noise of a single-mode laser operating at a low intensity level near the lasing threshold. A delayed self-heterodyning system has been developed to measure the random phase fluctuation. By actively stabilizing the phase of the interferometer, a random number generation rate of 500 Mbit/s has been demonstrated and the generated random numbers have passed all the DIEHARD tests.
The speed of a quantum random number generator is essential for practical applications, such as high-speed quantum key distribution systems. Here, we push the speed of a quantum random number generator to 68 Gbps by operating a laser around its threshold level. To achieve the rate, not only high-speed photodetector and high sampling rate are needed but also a very stable interferometer is required. A practical interferometer with active feedback instead of common temperature control is developed to meet the requirement of stability. Phase fluctuations of the laser are measured by the interferometer with a photodetector and then digitalized to raw random numbers with a rate of 80 Gbps. The min-entropy of the raw data is evaluated by modeling the system and is used to quantify the quantum randomness of the raw data. The bias of the raw data caused by other signals, such as classical and detection noises, can be removed by Toeplitz-matrix hashing randomness extraction. The final random numbers can pass through the standard randomness tests. Our demonstration shows that high-speed quantum random number generators are ready for practical usage.
Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth ≈\approx≈ 5.23 GHzGHzGHz) operated near threshold and a $\sim$48 cmcmcm fiber delay line, a raw data generation rate of 2.0 GbpsGbpsGbps is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 GbpsGbpsGbps in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.
We present a simple approach to realize truly random number generator based on measuring the phase noise of a single-mode vertical cavity surface emitting laser. The true randomness of the quantum phase noise originates from the spontaneous emission of photons and the random bit generation rate is ultimately limited only by the laser linewidth. With the final bit generation rate of 20 Mbit/s, the truly random bit sequence guaranteed by the uncertainty principle of quantum mechanics passes the three standard randomness tests (ENT, Diehard, and NIST Statistical Test Suites). Moreover, a continuously generated random bit sequence, with length up to 14 Gbit, is verified by two additional criteria for its true randomness.
In 2010 Qi et al. [Opt. Lett.35(3), 312 (2010)] demonstrated a random number generator based on the drift of the phase of a laser due to spontaneous emission, The out-of-the-lab implementation of this scheme presents two main drawbacks: it requires a long and highly unbalanced interferometer to generate a random phase with uniform probability distribution, or alternatively, a shorter and slightly unbalanced interferometer that notwithstanding requires active stabilization and does not generate a uniform probability distribution without randomness extraction. Here we demonstrate that making use of the random nature of the phase difference between two independent laser sources and two coherent detectors we can overcome these limitations. The two main advantages of the system demonstrated are: i) it generates a probability distribution of quantum origin which is intrinsically uniform and thus in principle needs no randomness extraction for obtaining a uniform distribution, and ii) the phase is measured with telecom equipment routinely used for high capacity coherent optical communications. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of the lasers. As a by-product of our method, we have obtained images of how phase noise develops with time in a laser. This provides a highly visual alternative way of measuring the coherence time of a laser.