On the capacities of bipartite Hamiltonians and unitary gates

Creators: Bennett, Charles H.; Harrow, Aram W.; Leung, Debbie W.; Smolin, John A.

Abstract

We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.

Additional Information

© Copyright 2005 IEEE. Reprinted with permission. Manuscript received September 16, 2002; revised April 4, 2003. [Posted online: 2003-07-22] This work was supported in part by the NSA under the U.S. Army Research Office (ARO) under Grants DAAG55-98-C-0041 and DAAD19-01-1-06. Communicated by P. W. Shor, Associate Editor for Quantum Information Theory. We wish to thank M. Leifer, L. Henderson, and N. Linden for discussions and for kindly sharing their results on entanglement capacity prior to publication. We also thank the above, as well as L. Spector and H. Bernstein, and K. Hammerer, G. Vidal, and J. I. Cirac for communicating their results on classical communications with bidirectional channels. We are indebted to many colleagues for their inputs to our work. We thank P. Shor for communicating his RSP results which are crucial to our results. We thank A. Childs and H.-K. Lo for their critical reading of the manuscript and for many constructive suggestions, part of which motivated a more precise version of Theorem 1 and the problem on d1 x d2 systems. The finiteness of the Hamiltonian capacities was questioned by G. Vidal, who also provided the proof for the finiteness of entanglement capacity. We wish to thank M. Nielsen for his upper bound on the entanglement capacity in terms of the Schmidt number. We wish to thank I. Devetak for important input in proving Bound 2; D. DiVincenzo, J. Dodd, J. Eisert, A. Kitaev, B. Terhal, and other members of the IQI at Caltech for additional helpful discussions. Since this paper was first posted, other related results have been posted [50], [56], [57], [58].

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