Reversible simulation of bipartite product Hamiltonians

Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.