We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement or classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems A and B interact by a nonlocal Hamiltonian H≠HA+HB . We consider the achievable space of Hamiltonians H8 such that the evolution e2iH8t can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H8, there exists a scale factor s such that for all times t the evolution e2iH8st can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H8, we calculate the optimal s and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of two-qubit Hamiltonians.
Bennett, C.H., Cirac, J.I., Leifer, M.S., Leung, D.W., Linden, N., Popescu, S., Vidal, G., 2002. Optimal simulation of two-qubit Hamiltonians using general local operations. Phys. Rev. A 66, 012305. doi:10.1103/PhysRevA.66.012305
American Physical Society