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Characterization of Gaussian operations and distillation of Gaussian states

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons60510

Giedke,  Géza
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons60441

Cirac,  J. Ignacio
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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Giedke, G., & Cirac, J. I. (2002). Characterization of Gaussian operations and distillation of Gaussian states. Physical Review A, 66(3): 032316. 032316. Retrieved from http://link.aps.org/abstract/PRA/v66/e032316.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-C1CF-3
Abstract
We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations that can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes that can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.