Full counting statistics of information content

TL;DR

This paper explores the relationship between full counting statistics and Rényi entanglement entropy, providing methods to calculate and analyze information content in quantum systems, especially for bosonic particles in communication channels.

Contribution

It introduces a path-integral approach on Keldysh contours to connect cumulant generating functions with Rényi entropy and analyzes information content fluctuations in bosonic channels.

Findings

The probability distribution of self-information can be derived from the information generating function.

Fluctuations in the information content ratio increase with lower boson occupation numbers.

The approach enables analysis of information content in nonequilibrium quantum steady states.

Abstract

We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the R\'enyi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.