  TThe problem of finding the resource free, closest local unitary, to any
bipartite unitary gate $U$ is addressed. Previously discussed as a measure of
nonlocality, the distance $K_D(U)$ to the nearest product unitary has
implications for circuit complexity and related quantities. Dual unitaries,
currently of great interest in models of complex quantum many-body systems, are
shown to have a preferred role as these are maximally and equally away from the
set of local unitaries. This is proved here for the case of qubits and we
present strong numerical and analytical evidence that it is true in general. An
analytical evaluation of $K_D(U)$ is presented for general two-qubit gates. For
arbitrary local dimensions, that $K_D(U)$ is largest for dual unitaries, is
substantiated by its analytical evaluations for an important family of
dual-unitary and for certain non-dual gates. A closely allied result concerns,
for any bipartite unitary, the existence of a pair of maximally entangled
states that it connects. We give efficient numerical algorithms to find such
states and to find $K_D(U)$ in general.
