Cumulant Structures of Entanglement Entropy

TL;DR

This paper introduces a novel method for deriving exact cumulant expressions of von Neumann entropy, revealing hidden structures and simplifying higher-order calculations in quantum information theory.

Contribution

The paper presents a new summation-free approach to compute higher-order cumulants of von Neumann entropy, overcoming limitations of existing methods.

Findings

Unveiled hidden cumulant structures in von Neumann entropy

Developed a summation-free method for higher-order cumulant calculation

Enabled exact derivation of cumulants of any order

Abstract

We present a new method to derive exact cumulant expressions of any order of von Neumann entropy over Hilbert-Schmidt ensemble. The new method uncovers hidden cumulant structures that decouple each cumulant in a summation-free manner into its lower-order joint cumulants involving families of ancillary statistics. Importantly, the new method is able to avoid the seemingly inevitable task of simplifying nested summations of increasing difficulty that prevents the existing method in the literature to obtain higher-order cumulants.