paper

On the impossibility of distilling Gaussian states with Gaussian operations

arXiv:quant-ph/0204052 · doi:10.1103/PhysRevLett.89.137903

Abstract

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.

4 pages, 1 colour figure. This paper is closely related to [J. Fiurasek, PRL 89, 137904 (2002), quant-ph/0204069] and to [G. Giedke and J.I. Cirac, PRA 66, 032316 (2002), quant-ph/0204085]. In particular, the latter paper arrives with independent methods at the general result that distillation is not possible for an arbitrary number of input copies and general Gaussian operations. The title of our contribution in its printed version has been changed by the editors of Physical Review Letters

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