Weight of quadratic forms and graph states

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.

8 pages, 3 eps figure, REVTeX; v2: We have extended the introduction, included extra references and added two figures; v3: small typos fixed