Quantum Grid States and Hybrid Graphs

TL;DR

This paper explores how various types of graphs, including hybrid and hypergraphs, can be used to interpret and construct complex quantum grid states with rich entanglement properties, advancing both quantum information and graph theory.

Contribution

It introduces new graph-based interpretations of grid states, including hybrid and hypergraphs, and develops techniques for constructing bound entangled states.

Findings

Hybrid graphs provide the most general interpretation of grid states.

Graphical methods can characterize and construct bound entangled states.

The work extends grid states to hypergraphs, enriching quantum state models.

Abstract

Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement properties of grid states are adapted to these interpretations. These additional classes of grid states are shown to exhibit rich entanglement properties, including bound entanglement. Further, we introduce graphical techniques to construct bound entangled states in a modular fashion. We also extend the grid states model to hypergraphs. Our work, on one hand, opens up possibilities for constructing additional families of mixed quantum states in the grid state model. On the other hand, it can serve as an instrument for investigating entanglement problems from a graph theory perspective.