  Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$
that couples them. We investigate the use of local operations and classical
communication (LOCC), together with the Hamiltonian $H$, to simulate a unitary
evolution of the $N$ systems according to some other Hamiltonian $H'$. First,
we show that the most general simulation using $H$ and LOCC can be also
achieved, with the same time efficiency, by just interspersing the evolution of
$H$ with local unitary manipulations of each system and a corresponding local
ancilla (in a so-called LU+anc protocol). Thus, the ability to make local
measurements and to communicate classical information does not help in
non--local Hamiltonian simulation. Second, we show that both for the case of
two $d$-level systems ($d>2$), or for that of a setting with more than two
systems ($N>2$), LU+anc protocols are more powerful than LU protocols.
Therefore local ancillas are a useful resource for non--local Hamiltonian
simulation. Third, we use results of majorization theory to explicitly solve
the problem of optimal simulation of two-qubit Hamiltonians using LU
(equivalently, LU+anc, LO or LOCC).
