Full counting statistics of information content in the presence of Coulomb interaction

TL;DR

This paper computes the full counting statistics of information content in a quantum dot system with Coulomb interaction, revealing how interactions influence rare events and bounds of the probability distribution of self-information.

Contribution

It introduces a method to calculate the Rénnyi entropy using a modified Keldysh Green function matrix and explores the impact of Coulomb interaction on information statistics.

Findings

Coulomb interaction affects the probability distribution of self-information.

A bound on the probability distribution is modified by interactions.

For noninteracting electrons, entanglement entropy relates to current cumulants.

Abstract

We calculate the R\'enyi entropy of a positive integer order $M$ for a reduced density matrix of a single-level quantum dot connected to left and right leads. We exploit a $2 \times 2$ modified Keldysh Green function matrix obtained by the discrete Fourier transform of a $2 M \times 2M$ multi-contour Keldysh Green function matrix. A moment generating function of self-information is deduced from the analytic continuation of $M$ to the complex plane. We calculate the probability distribution of self-information and find that, within the Hartree approximation, the on-site Coulomb interaction affects rare events and modifies a bound of the probability distribution. A simple equality, from which an upper bound of the average, i.e., the entanglement entropy, would be inferred, is presented. For noninteracting electrons, the entanglement entropy is expressed with current cumulants of the full-counting statistics of electron transport.