Geometry and Curvature of Spin Networks

TL;DR

This paper introduces a geometric framework based on quantum information transfer capacity to analyze spin networks, revealing their structure and limitations, and proposing control methods to enhance information transfer efficiency.

Contribution

It defines a new metric on spin networks derived from quantum information transfer, studies their geometry and curvature, and explores control strategies to improve transfer speed.

Findings

The metric induces a meaningful geometric structure on spin networks.

Hierarchical clustering reveals node proximities related to ITC.

Minimal control can significantly speed up quantum information transfer.

Abstract

A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg couplings. The geometry and curvature of spin chains with respect of this metric are studied and compared to the physical network geometry. For general networks hierarchical clustering is used to elucidate the proximity of nodes with regard to the maximum ITC. Finally, it is shown how minimal control can be used to overcome intrinsic limitations and speed up information transfer.