Anderson localisation in spin chains for perfect state transfer

TL;DR

This paper investigates Anderson localisation in disordered spin chains used for quantum state transfer, demonstrating localisation effects, transport delays, and spectral changes, establishing thresholds for localisation in quantum information systems.

Contribution

It provides the first extensive analysis linking Anderson localisation to quantum spin chains used for perfect state transfer, including thresholds and spectral effects.

Findings

Demonstrates spatial localisation in disordered spin chains

Identifies thresholds for Anderson localisation in quantum systems

Shows disorder impacts eigenstates and energy spectra

Abstract

Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for quantum information transport, and in particular can be engineered to allow for "perfect state transfer" (PST). Here we present extensive investigations of disordered PST spin chains, demonstrating spatial localisation and transport retardation effects, and relate these effects to conventional Anderson localisation. We provide thresholds for Anderson localisation in these finite quantum information systems for both the spatial and the transport domains. Finally, we consider the effect of disorder on the eigenstate and energy spectrum of our Hamiltonian, where results support our conclusions on the presence of Anderson localisation.