Optimising Perfect Quantum State Transfer for Timing Insensitivity

When studying the perfect transfer of a quantum state from one site to another, it is typically assumed that one can receive the arriving state at a specific instant in time, with perfect accuracy. Here, we study how sensitive perfect state transfer is to that timing. We design engineered spin chains which reduce their sensitivity, proving that this construction is asymptotically optimal. The same construction is applied to the task of creating superpositions, also known as fractional revival.