A de Bruijn identity for discrete random variables

Abstract

We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.

9 pages, shorter version submitted to ISIT 2017

References in corpus (2)

• Thinning, photonic beamsplitting, and a general discrete entropy power inequality
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels

Cited by in corpus (1)

• Gaussian optimizers for entropic inequalities in quantum information