Nonlocal Hamiltonian simulation assisted by local operations and classical communication

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 also be achieved, with the same time efficiency, by just interspersing the evolution of H with local unitary manipulations (LU) 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 nonlocal 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 nonlocal 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).