We establish natural connections between continuous-time Gaussian feedback/memory channels and their associated discrete-time versions in the forms of sampling and approximating theorems. It turns out that these connections, together with relevant tools from stochastic calculus, can enhance our understanding of continuous-time Gaussian channels in terms of giving alternative interpretations to ...

The average of integer powers of the Gaussian Q-function over fading distributions is commonly found in the evaluation of the average error performance of wireless communication systems over fading channels. Expressions known in the literature for η-μ and κ-μ fading channels only include solutions for the average of one Gaussian Q-function and the product of two Gaussian Q-functions. This Lette...

A complete weak-degradability analysis of one-mode Gaussian Bosonic channels is performed. A new set of channels which have null quantum capacity is identified. Due to their relatively simple structure Gaussian channels [1] provide an ideal theoretical playground for the study of quantum communication protocols [2]. Bounds and, in some cases, explicit values for the classical [3] or quantum [4]...

For vector Gaussian channels, a precise differential connection between channel capacity and a quantity termed normalized optimal detection error (NODE) is presented. Then, this C–NODE relationship is extended to continuous-time Gaussian channels drawing on a waterfilling characterization recently found for the capacity of continuous-time linear time-varying channels. In the latter case, the C–...

We show that the minimum output entropy for all single-mode Gaussian channels is additive and is attained for Gaussian inputs. This allows the derivation of the channel capacity for a number of Gaussian channels, including that of the channel with linear loss, thermal noise, and linear amplification.

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construc...

A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes that is needed is identified, including all rank deficient cases, and the specific role of additive classical noise is highlighted. By using this ...

In this paper, we propose a Polar coding scheme for parallel Gaussian channels. The encoder knows the sum rate of the parallel channels but does not know the rate of any channel. By using the nesting property of Polar code, we design a coding/decoding scheme to achieve the sum rates. Keywords-Polar codes; Paralle Gaussian channels.

A classification of one-mode Gaussian channels is given up to canonical unitary equivalence. A complementary to the quantum channel with additive classical Gaussian noise is described providing an example of onemode Gaussian channel which is neither degradable nor anti-degradable. 1 The canonical form For a mathematical framework of linear Bosonic system used in this note the reader is referred...

We identify the quantum channels corresponding to the interaction of a Gaussian quantum state with an already formed Schwarzschild black hole. Using recent advances in the classification of one-mode bosonic Gaussian channels, we find that (with one exception) the black hole Gaussian channels lie in the nonentanglement breaking subset of the lossy channels CðlossÞ, amplifying channels CðampÞ and...