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Abstract
We introduce the interaction cost of a non-local gate as the minimal time of interaction
required to perform the gate when assisting the process with fast local unitaries.
This cost, of interest both in the areas of quantum control and quantum information,
depends on the specific interaction, and allows to compare in an operationally meaningful
manner any two non-local gates. In the case of a two-qubit system, an analytical expression
for the interaction cost of any unitary operation given any coupling Hamiltonian is
obtained. One gate may be more time-consuming than another for any possible interaction.
This defines a partial order structure in the set of non-local gates, that compares
their degree of non-locality. We analytically characterize this partial order in a
region of the set of two-qubit gates.