Weight of quadratic forms and graph states

TL;DR

This paper establishes a link between the Schmidt-rank and the weight of quadratic forms, offering a new method for classifying graph states by their entanglement properties and characterizing functions related to bipartite graph pivot-minors.

Contribution

It introduces a novel connection between quadratic form weights and graph state entanglement, enhancing classification techniques and simplifying related function characterizations.

Findings

Connected Schmidt-rank with quadratic form weight for graph states

Provided a new classification tool for entanglement in graph states

Characterized functions associated with bipartite graph pivot-minors

Abstract

We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.