  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.
