Information Transfer Fidelity in Spin Networks and Ring-based Quantum Routers

TL;DR

This paper analyzes the limits of information transfer in spin networks, establishing conditions for optimal transfer fidelity, and proposes control strategies to enhance transfer times and fidelities in quantum routing.

Contribution

It introduces a dynamical model for achieving maximum transfer probability and shows how simple controls can improve quantum information routing in spin networks.

Findings

Maximum transfer fidelity can be asymptotically reached under specific conditions.

Simple spatially localized bias fields can significantly improve transfer fidelity and time.

A metric space framework for ring networks enables better understanding of transfer limitations.

Abstract

Spin networks are endowed with an Information Transfer Fidelity (ITF), which defines an absolute upper bound on the probability of transmission of an excitation from one spin to another. The ITF is easily computable but the bound can be reached asymptotically in time only under certain conditions. General conditions for attainability of the bound are established and the process of achiev-ing the maximum transfer probability is given a dynamical model, the translation on the torus. The time to reach the maximum probability is estimated using the simultaneous Diophantine approximation, implemented using a variant of the Lenstra-Lenstra-Lovasz (LLL) algorithm. For a ring with uniform couplings, the network can be made a metric space by defining a distance (satisfying the triangle inequality) that quantifies the lack of transmission fidelity between two nodes. It is shown that transfer fidelities and transfer times can be improved significantly by means of simple controls taking the form of non-dynamic, spatially localized bias fields, opening up the possibility for intelligent design of spin networks and dynamic routing of information encoded in them, while being more flexible than engineering fixed couplings to favor some transfers, and less demanding than control schemes requiring fast dynamic controls.