The transmission of information has gone through various stages of evolution throughout its history. A stage before that of the electric telegraph was the so-called aerial/optical telegraph. It was developed towards the end of the 18 century and was in service until the middle of the 19 century. Chappe’s system was widely used in France, and was the first to be in consistent use. However, a new...

We establish a probabilistic representation for a wide class of linear deterministic p.d.e.s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies to the heat equation, where it is related to the classical Feynman-Kac formula, as well as to the telegraph and beam equations. If the potential is a (random) spatially homogeneous Gaussian noise, t...

Solid state qubits promise the great advantage of being naturally scalable to large quantum computer architectures, but they also possess the significant disadvantage of being intrinsically exposed to many sources of noise in the macroscopic solid-state environment. With suitably chosen systems such as superconductors, many of sources of noise can be suppressed. However, imprecision in nanofabr...

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist deriving a general partial differential Equation (PDE) for the probability density (pdf) transformed process, and then presenting limiting PDE under Kac’s conditions, which may be interpreted as equation diffusion process on circle. This case includes, example, cases, such geometric Br...