Geometry and Curvature of Spin Networks

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.

6 pages, several figures and tables, IEEE tex

References in corpus (4)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• Euclidean versus hyperbolic congestion in idealized versus experimental networks
• Fast, high fidelity information transmission through spin chain quantum wires

Cited by in corpus (5)

• Jonckheere-Terpstra test for nonclassical error versus log-sensitivity relationship of quantum spin network controllers
• Structured singular value analysis for spintronics network information transfer control
• Curvature of quantum rings
• Characterization and Control of Quantum Spin Chains and Rings
• Routing a quantum state in a bio-inspired network