A bonding model of entanglement for $N$-qubit graph states

TL;DR

This paper introduces a bonding model for entanglement in $N$-qubit graph states, providing a clear physical interpretation of bonds, their creation and destruction, and their invariance under local unitary operations, with visual representation via color multigraphs.

Contribution

The paper presents a novel bonding model that characterizes entanglement in graph states through bonds, offering insights into their structure and invariance properties.

Findings

Bond presence indicates entanglement between qubits.

Local unitaries do not alter bond structures.

Color multigraphs effectively depict bond structures.

Abstract

The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum mechanics. A review of the properties of graph states is given and core spaces of graph states are introduced and discussed. A bonding model of entanglement for generalized graph states is then presented, in which the presence or absence of a bond between two qubits unequivocally specifies whether or not they are entangled. A physical interpretation of these bonds is given, along with a characterization of how they can be created or destroyed by entangling unitary operations and how they can be destroyed by local Pauli measurements. It is shown that local unitary operations do not affect the bond structure of a graph state, and therefore that if two graph states have nonisomorphic bond structures, then local unitary operations and/or reordering of qubits cannot change one into the other. Color multigraphs are introduced to depict the bond structures of graph states and to make some of their properties more apparent.