True randomness does not exist in classical physics, where randomness is necessarily a result of forces that may be unknown but exist. The quantum world, however, is intrinsically truly random. This is difficult to prove, as it is not readily distinguishable from noise and other uncontrollable factors. Now Pironio et al. present proof of a quantitative relationship between two fundamental concepts of quantum mechanics — randomness and the non-locality of entangled particles. They first show theoretically that the violation of a Bell inequality certifies the generation of new randomness, independently of any implementation details. To illustrate the approach, they then perform an experiment in which — as confirmed using the theoretical tools that they developed — 42 new random bits have been generated. As well as having conceptual implications, this work has practical implications for cryptography and for numerical simulation of physical and biological systems. Here it is shown, both theoretically and experimentally, that non-local correlations between entangled quantum particles can be used for a new cryptographic application — the generation of certified private random numbers — that is impossible to achieve classically. The results have implications for future device-independent quantum information experiments and for addressing fundamental issues regarding the randomness of quantum theory. Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically1, and their generation must rely on an unpredictable physical process2,3,4,5,6. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based7,8,9 and device-independent10,11,12,13,14 quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation15. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.

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Random numbers certified by Bell's theorem.

This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.

Physics and applications of laser diode chaos

Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

In mathematics and computer science, random numbers have the role of a resource for assisting proofs, making cryptography secure, and enabling computational protocols. This role motivates efforts to produce random numbers as a physical process. Potential physical sources abound, but arguably the most fundamental are those based on elementary quantum mechanical processes. This review discusses the current status of devices that generate quantum random numbers.

Quantum random number generators

The generation of random bit sequences at a data rate of up to 300 Gbit s−1 — a rate many orders of magnitude faster than previously achieved — is realized by exploiting the output of a chaotic semiconductor laser. The randomness of the generated bits is verified by standard statistical tests.

An optical ultrafast random bit generator

Random number generators in digital information systems make use of physical entropy sources such as electronic and photonic noise to add unpredictability to deterministically generated pseudo-random sequences1,2. However, there is a large gap between the generation rates achieved with existing physical sources and the high data rates of many computation and communication systems; this is a fundamental weakness of these systems. Here we show that good quality random bit sequences can be generated at very fast bit rates using physical chaos in semiconductor lasers. Streams of bits that pass standard statistical tests for randomness have been generated at rates of up to 1.7 Gbps by sampling the fluctuating optical output of two chaotic lasers. This rate is an order of magnitude faster than that of previously reported devices for physical random bit generators with verified randomness. This means that the performance of random number generators can be greatly improved by using chaotic laser devices as physical entropy sources. Random-number generators are important in digital information systems. However, the speed at which current sources operate is much slower than the typical data rates used in communication and computing. Chaos in semiconductor lasers might help to bridge the gap.

Takayuki Kurashige

Papers

Fast physical random bit generation with chaotic semiconductor lasers