Optimal simulations of two-qubit Hamiltonians using general local operations

CH Bennett, JI Cirac, MS Leifer, DW Leung, N Linden, S Popescu, G Vidal

Research output: Contribution to journalArticle (Academic Journal)

85 Citations (Scopus)

Abstract

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 Hnot equalH(A)+H-B. We consider the achievable space of Hamiltonians H-' such that the evolution e(-iH')t can be simulated by the interaction H interspersed with local operations. For any dimensions of A and B, and any nonlocal Hamiltonians H and H-', there exists a scale factor s such that for all times t the evolution e(-iH')st can be simulated by H acting for time t interspersed with local operations. For two-qubit Hamiltonians H and H-', 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.
Translated title of the contributionOptimal simulations of two-qubit Hamiltonians using general local operations
Original languageEnglish
Article numberArt. No. 012305
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Volume66 (1)
Publication statusPublished - Jul 2002

Bibliographical note

Publisher: American Physical Soc
Other identifier: IDS number 579WH

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