Random Processes

Yujie Luo, Yang Li, Jie Yang +3 more

As one of the applications of randomness extraction, post-processing is important for the high-speed and real-time QRNG (Quantum Random Number Generator) system. This work proposes a multi-thread and streamed-processing algorithm to optimize post-processing based on Toeplitz matrix on GPU (Graphics Processing Unit) and achieves a high speed over 6.8 Gbps. Furthermore, random tests are done to evaluate the quality of the random bits generated. The results show that both the execution speed and the randomness can satisfy the requirements of the high-speed and real-time QRNG system.

Philippe Réfrégier

Leonard Mandel, E. Wolf

Introduction to statistical ensembles The concept of a random or stochastic process or function represents a generalization of the idea of a set of random variables x 1 , x 2 , …, when the set is no longer countable and the variables form a continuum. We therefore introduce a continuous parameter t , such as time, that labels the variates. We call x ( t ) a random process or a random function of t if x does not depend on t in a deterministic way. Random processes are encountered in many fields of science, whenever fluctuations are present. Examples of a real random process x ( t ) are the fluctuating voltage across an electrical resistor, and the coordinates of a particle under-going Brownian motion. We shall see shortly that the optical field generated by any realistic light source must also be treated as a random function of position and time. Of course the parameter t may also stand for some quantity other than time, but for simplicity we shall take it to represent time. In our applications x ( t ) will frequently represent a Cartesian component of the electric or magnetic field vector in a light beam. To begin with we shall take x ( t ) to be real, but complex random processes will also be encountered. The ensemble average As x does not depend on t deterministically, we can only describe its values statistically, by some probability distribution or probability density.

Roberto Piazza

Tânia Tomé, Mário J. de Oliveira

Seok Hyung Lie, Hyunseok Jeong

Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we generalize this result to general randomness-utilizing processes and show that the gap between the efficiencies of classical and quantum catalytic randomness is generic. To explore the achievability of catalysis of quantum randomness, we first show that the second law of thermodynamics holds for general randomness-utilizing processes: the amount of randomness never decreases. Especially, for two important randomization processes, dephasing and erasure maps, randomness sources are forced to be used catalytically, i.e., in such a way that the randomness is preserved exactly. Second, we show that non-degenerate catalysts should be used classically, which leads to the fact that the quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source. Finally, we discuss a method to circumvent the previous result that achieves quantum advantage with non-degenerate catalyst uniformized by employing extra work space.