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arXiv:1604.01915 · Physical Review A

More randomness from a prepare-and-measure scenario with independent devices

Yun-Guang Han, Zhen−Qiang Yin, Hong-Wei Li, Wei Chen, Shuang Wang, Guang‐Can Guo, Zheng‐Fu Han

Published Mar 22, 2016• 9 citations
arXivHTMLPDF

Abstract

How to generate genuine quantum randomness from untrusted devices is an important problem in quantum information processing. Inspired by previous work on a self-testing quantum random number generator [T. Lunghi et al., Phys. Rev. Lett. 114, 150501 (2015)], we present a method to generate quantum randomness from a prepare-and-measure scenario with independent devices. In existing protocols, the quantum randomness depends only on a witness value (e.g., Clauser-Horne-Shimony-Holt value), which is calculated with the observed probabilities. Differently, here all the observed probabilities are directly used to calculate the min-entropy in our method. Through numerical simulation, we find that the min-entropy of our proposed scheme is higher than that in the previous work when a typical untrusted Bennett-Brassard 1984 (BB84) setup is used. Consequently, thanks to the proposed method, more genuine quantum random numbers may be obtained than before.

DOI
10.1103/physreva.93.032332

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How to generate genuine quantum randomness from untrusted devices is an important problem in quantum information processing. Inspired by previous work on a self-testing quantum random number generator [T. Lunghi et al., Phys. Rev. Lett. 114, 150501 (2015)], we present a method to generate quantum randomness from a prepare-and-measure scenario with independent devices. In existing protocols, the quantum randomness depends only on a witness value (e.g., Clauser-Horne-Shimony-Holt value), which is calculated with the observed probabilities. Differently, here all the observed probabilities are directly used to calculate the min-entropy in our method. Through numerical simulation, we find that the min-entropy of our proposed scheme is higher than that in the previous work when a typical untrusted Bennett-Brassard 1984 (BB84) setup is used. Consequently, thanks to the proposed method, more genuine quantum random numbers may be obtained than before.
Quantum random number generation attracts considerable attention, since its randomness inherently originates in quantum mechanics, but not mathematical assumptions. Randomness certification, e.g. entropy estimation, becomes a key issue in the context of quantum random number generation protocol. We study a self-testing protocol based on dimension witness, with the assumption of independent devices. It addresses the random number extraction problem in a practical prepare-and-measure scenario with uncharacterized devices. However, the lower bound of min-entropy as a function of dimension witness is not tight in existing works. We present a tighter bound of analytic form, by introducing the Lagrangian multiplier method to closely analyze the optimization problem on average guessing probability. Through simulation, it turns out that a significantly higher random number generation rate can be achieved in practice.
How to estimate the randomness of the measurement outcomes generated by a given device is an important issue in quantum information theory. Recently, Brunner et al. [Phys. Rev. Lett. 112 (2014) 140407] proposed a prepare-and-measure quantum random number generation scenario with device-independent assumption, which indicates a method to test the randomness of bit strings according to the generation process rather than the results. Based on this protocol, we implement a quantum random number generator with an intrinsic stable phase-encoded quantum key distribution system. The system has been continuously running for more than 200 h, a stable witness W with the average value of 0.9752 and a standard deviation of 0.0024 are obtained. More than 1 G random bits are generated and the results pass all items of NIST test suite.
Quantum random number generators (QRNGs) play an increasingly important role in cryptography systems. Specifically, QRNG performed in prepare-and-measure scenarios with independent devices has attracted intensive study, since it can be intrinsically loss tolerant and its assumptions on devices seem to be quite natural. However, the estimations of min-entropy given in previous works are not optimal. As a result, the performance of quantum randomness certification in practice is still severely depressed. Here, we present a novel method to estimate the min-entropy through developing a reduced device model and proving its equivalence to the original one. Benefitting from this reduction, we can solve the min-entropy estimation problem using mixed integer programming effectively. Furthermore, we derive an optimal bound of analytic form in the case that constraints are made up of symmetric observed probabilities. Simulation results show that our work gives an optimal solution in this case and brings a significant performance improvement compared to previous works.
The random number is a paramount issue in modern science. How to estimate the genuine randomness of the data generated by a given device is a central problem. Lunghi et al. proposed a self-testing quantum random number generator from a prepare-and-measure scenario with independent devices. Based on this Letter, Han et al. proposed a more efficient method (Han16 protocol for short) to estimate the genuine randomness. Here we report a proof-of-principle realization of the Han16 protocol with a HSPS. The experimental results demonstrate that the Han16 protocol almost doubles the generation rate of the quantum random number with regard to the previous protocol. In addition, the results of the experiment show that the Han16 protocol is practical, and the experimental device can tolerate loss and noise.
It is a well-known fact in classical information theory that no deterministic procedure can extract close-to-ideal randomness from an arbitrary entropy source. On the other hand, if additional knowledge about the source is available -- e.g., that it is a sequence of independent Bernoulli trials -- then deterministic extractors do exist. For quantum entropy sources, where in addition to classical random variables we consider quantum side information, the use of extra knowledge about their structure was pioneered in a recent publication [C. Foreman and L. Masanes, Quantum 9, 1654 (2025)]. In that work, the authors provide deterministic extractors for device-independent randomness generation with memoryless devices achieving a sufficiently high CHSH score. In this work, we port their construction to the prepare-and-measure scenario. Specifically, we prove that the considered functions are also extractors for memoryless devices in settings with partial trust, either in the state preparation or in the measurement, as well as in a semi-device-independent setting under an overlap assumption on the prepared quantum states. Within this last setting, we simulate the resulting randomness generation protocol on a novel and experimentally relevant family of behaviors, observing positive key rates already for 7×1037\times 10^37×103 rounds.
Measuring quantum states provides a means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized source by measuring two incompatible bases [Phys. Rev. X 6, 011020 (2016)]. As coherence is the necessary source for generating randomness, we extend the scheme and propose a framework for quantum random number generation with general uncharacterized coherence resource. The previous scheme can be treated as a special case under the framework by considering a nonlinear uncertainty-relation-based coherence witness. Considering general coherence witnesses, we propose a source-independent random-number generation scheme that achieves a higher randomness generation rate. Our paper highlights the close relation between coherence and random-number generation and may shed light on designing general semi-device-independent quantum information processing protocols.