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arXiv:1709.06779 · Physical Review Letters

High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole

Yang Liu, Xiao Yuan, Minghan Li, Weijun Zhang, Qi Zhao, Jiaqiang Zhong, Yuan Wen Cao, Yu-Huai Li, Luo-Kan Chen, Hao Li, Tianyi Peng, Yu-Ao Chen, Cheng-Zhi Peng, Sheng‐Cai Shi, Zhen Wang, Lixing You, Xiongfeng Ma, Jingyun Fan, Qiang Zhang, Jian-Wei Pan

Published Jan 3, 2018• 140 citations
arXivHTMLPDF

Abstract

Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an 80 Gb×45.6 Mb Toeplitz matrix hashing, we achieve a final random bit rate of 114 bits/s, with a failure probability less than 10^{-5}. This marks a critical step towards realistic applications in cryptography and fundamental physics tests.

DOI
10.1103/physrevlett.120.010503

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Abstract From dice to modern electronic circuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable1–3. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity1–11. With recent technological developments, it is now possible to carry out such a loophole-free Bell test12–14, 22. Here we present certified randomness obtained from a photonic Bell experiment and extract 1, 024 random bits that are uniformly distributed to within 10−12. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.
Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 random bits with an average experiment time of less than 5 min per block and with a certified error bounded by 2^{-64}≈5.42×10^{-20}.
What is the most efficient way to generate random numbers deviceindependently using a photon pair source based on spontaneous parametric down conversion (SPDC)? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where nonlocality is revealed using photon counting preceded by small displacement operations. ar X iv :1 40 9. 80 51 v1 [ qu an tph ] 2 9 Se p 20 14 Device-independent quantum random number generator with a photon pair source 2 We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell-CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of both the entropy per experimental run and the rate of random bit generation. PACS numbers: 03.65.Ud Device-independent quantum random number generator with a photon pair source 3
Device-independent quantum random number generators (DI-QRNGs) are crucial for many information-processing applications, requiring certified quantumness to ensure genuine randomness. However, inherent technical challenges in implementing quantumness tests often result in a low bit rate. Here, we present a high-bit-rate DI-QRNG with live quantumness certification through the Bell test. By employing spontaneous parametric down-conversion (SPDC) in a polarization Sagnac interferometer, which generates entangled degenerate pair-photons in annular ring distribution with strong temporal and spatial correlations due to energy and momentum conservation, we divide the annular ring into six diametrically opposite sections, forming three robust entangled photon sources from a single laser and nonlinear crystal. The pair-photons from these three sources exhibit bias-free quantum mechanical randomness. By utilizing the coincidence counts of pair-photons from two sources, we generate raw bits, while the third source simultaneously measures the Bell’s parameter without any loss of QRNG bits. We have generated 90 million raw bits in 46.4 seconds with the Bell parameter (S > 2), with a minimum entropy extraction ratio exceeding 97%. Post-processed using a Toeplitz matrix, the DI-QRNG achieves a bit rate of 1.8 Mbps, passing all NIST 800-22 and TestU01 tests. In the absence of Bell’s parameter for a non-maximally entangled state, g (2) (0) can be the metric for quantumness measure. Free from the requirement of any physical devices such as beam-splitters, this scalable DI-QRNG scheme promises high bit-rates and trustworthy certifications essential for practical applications.