Entanglement dynamics of multi-parametric random states: a single parametric formulation

TL;DR

This paper develops a unified, parametric framework to analyze the entanglement dynamics of complex, multi-parametric random quantum states, resolving existing debates and providing new insights into their information growth.

Contribution

It introduces a generalized Wishart ensemble model for multi-parametric states and derives a common mathematical formulation for entanglement measures based on a complexity parameter.

Findings

Resolved controversy on entropy growth rates

Established a universal mathematical framework for entanglement measures

Provided insights into entanglement hierarchy and dynamics

Abstract

A non-ergodic quantum state of a many body system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.