Optimal experiments for maximizing coherence transfer between coupled spins

In spite of great advances in the theory and applications of magnetic resonance in the past 50 years, some basic questions in spin physics have not yet been answered. In the absence of relaxation losses, what is the maximum amount of coherence that can be transferred between coupled spins under general coupling tensors in a given time and how can this be realized experimentally? Since transfer of coherence between spins forms the basis for multidimensional experiments in NMR spectroscopy, the answers to these questions are of both practical and theoretical interest. Computing the physical limits of coherence transfer involves characterizing all unitary evolutions that can be synthesized in a given time. Here we derive these limits and show how they can be achieved experimentally.