Classical Hierarchical Correlation Quantification on Tripartite Qubit Mixed State Families

TL;DR

This paper introduces a classical hierarchical correlation measure for tripartite qubit mixed states, revealing how different entanglement types influence correlation quantification.

Contribution

It proposes a novel correlation quantification method based on von Neumann measurement statistics, applicable to specific tripartite qubit mixed state families, highlighting entanglement effects.

Findings

Correlation measure distinguishes different entanglement types

Method is sensitive to the structure of tripartite states

Results demonstrate correlation quantification reflects entanglement nature

Abstract

There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object itself. This is usually achieved by detecting and taking advantage of regularities within the object. Regularities can commonly be described in an information-theoretic approach by quantifying the amount of correlation playing a role in the system, this being spatial, temporal or both. This is the approach closely related to the extent that the whole cannot be understood as only the sum of its parts, but also by their interactions. Feature considered to be most fundamental. Nevertheless, this irreducibility, even in the basic quantum informational setting of composite states, is also present due to the intrinsic structure of Hilbert spaces' tensor product. In this approach, this irreducibility is quantified based on statistics of von Neumann measurements forming mutually unbiased bases. Upon two different kinds of tripartite qubit mixed state families, which hold the two possible distinct entangled states on this space. Results show that this quantification is sensible to the different kind of entanglement present on those families.