K.R. Parthasarathy’s contributions to quantum Gaussian distributions and applications

In the “short pedagogical essay” [1], published in 2010, K.R. Parthasarathy illustrated the notion of a quantum Gaussian state as a natural extension of the idea of Gaussian or normal distribution in classical probability. This presentation led to some interesting open problems on symmetry transformation and other properties of quantum Gaussian states, calling for further investigation which he continued in the following years.