Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts

TL;DR

This paper introduces new invariants based on negativity fonts for classifying four-qubit states, identifying a specific polynomial invariant that distinguishes states with four-body correlations and proposing a classification into seven major classes.

Contribution

It develops novel degree-specific invariants using negativity fonts and provides a new classification scheme for four-qubit states based on correlation properties.

Findings

Identified a degree 8 polynomial invariant distinguishing states with four-body correlations.

Constructed invariants of degrees 8, 12, and 24 for four-qubit states.

Proposed a classification of four-qubit states into seven major classes.

Abstract

Local unitary invariance and the notion of negativity fonts are used as the principle tools to construct four qubit invariants of degree 8, 12, and 24. A degree 8 polynomial invariant that is non-zero on pure four qubit states with four-body correlations and zero on all other states, is identified. Classification of four qubit states into seven major classes, using criterion based on the nature of correlations, is discussed.