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Physical Review Letters

Certified Randomness from Untrusted Sources and Uncharacterized Measurements

Xing Ping Lin, Rong Wang, Shuang Wang, Zhen−Qiang Yin, Wei Chen, Guang‐Can Guo, Zheng‐Fu Han

Published Jul 28, 2022• 27 citations
Publisher

Abstract

Generating random numbers plays an important role in many scientific applications. Compared to pseudorandom number generators, a quantum device is capable of generating true random numbers by the laws of quantum mechanics. However, information-theoretical secure random numbers are regularly based on a perfect device model, which may deviate from a real-world device. To close this gap, we propose a quantum random number generation protocol and experimentally demonstrate it. In our protocol, we make no assumptions about the source. Some reasonable assumptions on the trusted two-dimensional measurement are needed, but we do not require a detailed characterization. Even if considering the most general quantum attack and using the general sources, we achieve a randomness generation rate of over 1 Mbps with a universal composable security parameter of 10^{-10}.

DOI
10.1103/physrevlett.129.050506

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Generating random numbers plays an important role in many scientific applications. Compared to pseudorandom number generators, a quantum device is capable of generating true random numbers by the laws of quantum mechanics. However, information-theoretical secure random numbers are regularly based on a perfect device model, which may deviate from a real-world device. To close this gap, we propose a quantum random number generation protocol and experimentally demonstrate it. In our protocol, we make no assumptions about the source. Some reasonable assumptions on the trusted two-dimensional measurement are needed, but we do not require a detailed characterization. Even if considering the most general quantum attack and using the general sources, we achieve a randomness generation rate of over 1 Mbps with a universal composable security parameter of 10^{-10}.
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics.In general, a physical generator contains two parts-a randomness source and its readout.The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness.However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output.To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted.In our randomness analysis, we make no assumptions about the dimension of the source.For instance, multiphoton emissions are allowed in optical implementations.Our analysis takes into account the finite-key effect with the composable security definition.In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit.In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 × 10 3 bit=s.
A remarkable aspect of quantum theory is that certain measurement outcomes arc entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. We formally introduce, design, and experimentally demonstrate an ultrafast optical quantum random number generator that uses a totally untrusted photonic source. While considering completely general quantum attacks, we certify and generate in real time random numbers at a rate of 8.05 Gb/s with a composable security parameter of 10(-10). Composable security is the most stringent and useful security paradigm because any given protocol remains secure even if arbitrarily combined with other instances of the same, or other, protocols, thereby allowing the generated randomness to be utilized for arbitrary applications in cryptography and beyond. This work achieves the fastest generation of composably secure quantum random numbers ever reported.
Random number generation is vital for cryptography. The classical world faces inherent limitations in generating provably true random numbers. Quantum mechanics, however, provides a natural foundation for genuinely unpredictable outcomes. In random number generation protocols, source-independent protocols ensure security even with untrusted source devices. Hence, we propose a sourceindependent expansion protocol with partially free sources to balance security and feasibility. In our proposed protocol, an untrusted source is interrogated by trusted measurement devices, utilizing a partially free source for randomness expansion. Based on Quantum random access codes (QRACs) in a three-dimensional Hilbert space with partially free source, we construct a quantum witness, derive the relationship between randomness generation efficiency and the violation of this witness. This demonstrates the advantage of utilizing higher-dimensional systems to generate more certified randomness.
Quantum random number generators (QRNGs) use the inherent unpredictability of quantum mechanics to generate true randomness, as opposed to classical random number generators. However, ensuring the authenticity of this randomness still requires robust verification. Self-testing QRNGs address this need by enabling the validation of the randomness produced based on the observed data from the experiment while requiring few assumptions. In this work, we present a practical, self-testing QRNG designed to operate with an untrusted measurement device and a partially characterized source, allowing the user to check the adequate functioning of the setup in real time. Our experiment yields a rate of certified random bits of 450 kbps.
Quantum random number generators can provide genuine randomness by exploiting the intrinsic probabilistic nature of quantum mechanics, which play important roles in many applications. However, the true randomness acquisition could be subject to attacks from untrusted devices involved or their deviations from the theoretical modelling. Here we propose and experimentally demonstrate a source-device-independent quantum random number generator, which enables one to access true random bits with an untrusted source device. The random bits are generated by measuring the arrival time of either photon of the time-energy entangled photon pairs produced from spontaneous parametric down conversion, where the entanglement is testified through the observation of nonlocal dispersion cancellation. In experiment we extract a generation rate of 1.125 Mbps by modified entropic uncertainty relation. Our approach provides a promising candidate for quantum random number generators with no characterization.
Quantum random number generators (QRNGs) promise secure randomness generation based on the foundational unpredictability of quantum mechanics. However, the unavoidable gaps between theoretical models and practical devices could lead to security invalidation. Recently, a source-independent quantum random number generator (SI-QRNG) has been proposed to solve the issue of uncharacteristic sources. However, in most current analyses of SI-QRNG protocols, the security proofs with imperfect measurements are individual for different factors and very sensitive to small deviations from theoretical models. Here, we establish a unified model for imperfect measurements in the SI-QRNG and provide a tight rate bound based on the uncertainty relation for smooth entropies. Then the performance with large device imperfections is evaluated and the randomness rate in our model can approach a similar order of magnitude of the rate upper bound in common discrete variable QRNGs. In addition, by utilizing the daily illumination and measurement devices with large imperfections, we experimentally demonstrate our scheme at the rate of the order of magnitude of Mbps.