The Limits of Quantum State Transfer for Field-Free Heisenberg Chains

TL;DR

This paper demonstrates the impossibility of perfect quantum state transfer in field-free Heisenberg chains and explores alternative methods for high-quality transfer, including timing strategies for approximate transfer accuracy.

Contribution

It proves the non-existence of perfect transfer in such chains and introduces a new paradigm for estimating transfer times to achieve desired accuracy levels.

Findings

No coupling strengths enable perfect transfer without magnetic fields.

High-quality transfer can be approached through timing strategies.

A new paradigm for estimating transfer times based on target accuracy.

Abstract

In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of perfect transfer, we consider a range of options for achieving high quality transfer, whether in finite time, or via "pretty good" transfer where one waits long times in the hope of getting arbitrarily close to perfect transfer. In attempting to engineer arbitrarily accurate transfer, we explore a new paradigm that facilitates time estimates for achieving any target accuracy $\epsilon$ for the transfer.