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Causal and localizable quantum operations

Beckman, David and Gottesman, Daniel and Nielsen, M. A. and Preskill, John (2001) Causal and localizable quantum operations. Physical Review A, 64 (5). Art. No. 052309. ISSN 1050-2947. http://resolver.caltech.edu/CaltechAUTHORS:BECpra01

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Abstract

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate; it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semilocalizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.


Item Type:Article
Additional Information:©2001 The American Physical Society Received 9 February 2001; published 12 October 2001 We thank Harry Buhrman, Richard Cleve, and David DiVincenzo for helpful discussions, Jennifer Dodd for comments on the manuscript, and Reinhard Werner and Rainer Verch for instructive correspondence. This work has been supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, by the National Science Foundation, by IBM, and by the Clay Mathematics Institute. Some of this work was done at the Aspen Center for Physics.
Record Number:CaltechAUTHORS:BECpra01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BECpra01
Alternative URL:http://dx.doi.org/10.1103/PhysRevA.64.052309
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1989
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:28 Feb 2006
Last Modified:26 Dec 2012 08:47

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