Bounds on probability of state transfer with respect to readout time and edge weight

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.