Entanglement of N distinguishable particles

TL;DR

This paper critiques existing entanglement classifications for N distinguishable particles, introduces the concept of utter entanglement, and presents a new state example illustrating this nuanced entanglement structure.

Contribution

It proposes a refined categorization of entanglement by introducing the notion of utter entanglement, addressing gaps in previous classifications.

Findings

Identifies a missing case in entanglement classification.

Provides an example of a state with complete but not utter entanglement.

Introduces the concept of utter entanglement as a new classification.

Abstract

In their 2002 article, Ghirardi, Marinatto and Weber have proposed a formal analysis of the entanglement properties for a system consisting of N distinguishable particles. Their analysis leads to the differentiation of three possible situations that can arise in such systems: complete entanglement, complete non-entanglement, and the remaining cases. I argue that this categorization leaves out one important possibility in which a system is completely entangled, and yet some of its subsystems are mutually non-entangled. As an example I present and discuss a state of a three-particle system which cannot be decomposed into two non-entangled systems, and yet particle number one is not entangled with particle number three. Consequently, I introduce a new notion of utter entanglement, and I argue that some systems may be completely but not utterly entangled.