# Optimal Bounds on State Transfer Under Quantum Channels with Application to Spin System Engineering

## TL;DR

This paper establishes theoretical bounds on quantum state transfer efficiency across various quantum channels and demonstrates their application in optimizing control strategies in NMR experiments for spin system engineering.

## Contribution

It provides a comprehensive analysis of optimal state transfer bounds for different quantum channels and applies these results to enhance NMR quantum control techniques.

## Key findings

- Mixed unitary channels do not expand the state transfer region.
- Optimal experiment design improves transfer efficiency and reduces experiments.
- Pseudopure state preparation confirms theoretical bounds in practice.

## Abstract

Modern applications of quantum control in quantum information science and technology require the precise characterization of quantum states and quantum channels. In particular, high-performance quantum state engineering often demands that quantum states are transferred with optimal efficiency via realizable controlled evolution, the latter often modeled by quantum channels. When an appropriate quantum control model for an interested system is constructed, the exploration of optimal bounds on state transfer for the underlying quantum channel is then an important task. In this work, we analyze the state transfer efficiency problem for different class of quantum channels, including unitary, mixed unitary and Markovian. We then apply the theory to nuclear magnetic resonance (NMR) experiments. We show that two most commonly used control techniques in NMR, namely gradient field control and phase cycling, can be described by mixed unitary channels. Then we show that employing mixed unitary channels does not extend the unitarily accessible region of states. Also, we present a strategy of optimal experiment design, which incorporates coherent radio-frequency field control, gradient field control and phase cycling, aiming at maximizing state transfer efficiency and meanwhile minimizing the number of experiments required. Finally, we perform pseudopure state preparation experiments on two- and three-spin systems, in order to test the bound theory and to demonstrate the usefulness of non-unitary control means.