In a continuous-variable quantum key distribution (CVQKD) system, the information is conveyed by coherent state carriers. The quantum continuous variables are sent through a quantum channel, where the presence of the eavesdropper adds a white Gaussian noise to the transmission. The amount of tolerable noise and loss is a crucial point in CVQKD, since it determines the overall performance of the...

In recent years, several algorithms which approximate matrix decomposition have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We present a new algorithm, which achieves with high probability a rank-r SVD approximation of an n × n matrix and derive an error bound that does not depend on the first r singular values. Althou...

1 Deviation bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Markov and generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Class of sub-Gaussian random variables . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2....

We present a computationally efficient method to generate random variables from a univariate conditional probability density function (PDF) derived from a multivariate α-sub-Gaussian (αSG) distribution. The approach may be used to sequentially generate variates for sliding-window models that constrain immediately adjacent samples to be αSG random vectors. We initially derive and establish vario...

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...