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

References in corpus (4)

• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Entanglement in the stabilizer formalism
• Edge Local Complementation and Equivalence of Binary Linear Codes
• Quantum computing and polynomial equations over the finite field Z_2

Cited by in corpus (7)

• Graph Approach to Quantum Systems
• Arboreal Bound Entanglement
• On the local equivalence of complete bipartite and repeater graph states
• Graph state representation of the toric code
• Edge local complementation for logical cluster states
• Determination of stabilizer states
• Group structures and representations of graph states