Optimal simulation of nonlocal Hamiltonians using local operations and classical communication

Details Optimal simulation of nonlocal Hamiltonians using local operations and classical communication Optimal simulation of nonlocal Hamiltonians using local operations and classical communication

2001-08-16

arxiv.org/abs/quant-ph/0108076v2

Phys. Rev. A 66, 022315 (2002)

Physics

Quantum Physics

10 pages, 1 figure, revtex, major changes in presentation, results unchanged

Scientific paper

10.1103/PhysRevA.66.022315

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).

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