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Reversible simulation of bipartite product Hamiltonians

Childs, Andrew M. and Leung, Debbie W. and Vidal, Guifré (2004) Reversible simulation of bipartite product Hamiltonians. IEEE Transactions on Information Theory, 50 (6). pp. 1189-1197. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:CHIieeetit04

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Abstract

Consider two quantum systems A and B interacting according to a product Hamiltonian H = H-A circle times 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 nonlocal 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.


Item Type:Article
Additional Information:© Copyright 2004 IEEE. Reprinted with permission. Manuscript received March 27, 2003; revised July 22, 2003. The work of A. M. Childs was supported by the Fannie and John Hertz Foundation, and, in part, by the Cambridge-MIT Foundation, the Department of Energy under cooperative research agreement DE-FC02-94ER40818, and the National Security Agency and Advanced Research and Development Activity under Army Research Office Contract DAAD19-01-1-0656. The work of D. W. Leung and G. Vidal was supported by the National Science Foundation under Grant EIA-0086038. Communicated by E. H. Knill, Associate Editor for Quantum Information Theory.
Subject Keywords:channel capacity; entanglement; Hamiltonian simulation; quantum control; quantum information theory
Record Number:CaltechAUTHORS:CHIieeetit04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHIieeetit04
Alternative URL:http://dx.doi.org/10.1109/TIT.2004.828069
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2161
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Mar 2006
Last Modified:26 Dec 2012 08:47

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