Quantify the advantage of subensemble control over global control

Determine the extent to which independently controlling multiple subensembles enlarges the class of Hamiltonians engineerable by pulsed control compared with global control.

Background

The paper studies Hamiltonian engineering when global pulses can be applied independently to a small number of subensembles. This control model is more flexible than global control but substantially less demanding than fully site-resolved local control.

Although the paper establishes necessary and sufficient engineerability conditions for important classes of interaction matrices and develops numerical design methods, it does not provide a general characterization of how much more powerful subensemble control is than global control. The unresolved issue concerns the precise extent of the enlargement in the set of realizable Hamiltonians.