Bounds on probability of state transfer with respect to readout time and edge weight
Whitney Gordon, Steve Kirkland, Chi-Kwong Li, Sarah Plosker, and, Xiaohong Zhang
TL;DR
This paper investigates how small errors in readout time and edge weights affect the probability of perfect state transfer in spin chain models, providing bounds based on matrix numerical range and norms.
Contribution
It introduces bounds on state transfer probability considering perturbations, using numerical range and matrix norms, for more physically relevant analysis.
Findings
Bounds on state transfer probability under perturbations
Use of numerical range for sensitivity analysis
Application of spectral and Frobenius norms
Abstract
We analyse the sensitivity of a spin chain modelled by an undirected weighted connected graph exhibiting perfect state transfer to small perturbations in readout time and edge weight in order to obtain physically relevant bounds on the probability of state transfer. At the heart of our analysis is the concept of the numerical range of a matrix; our analysis of edge weight errors additionally makes use of the spectral and Frobenius norms.
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