On the distillation of Gaussian states with Gaussian operations
Abstract
We will 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 analysis shows that unlike the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time, there is no such procedure in the case of continuous variables for Gaussian initial states and the above Gaussian operations. The ramifications for the distribution of Gaussian states over large distances will be outlined. We will also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bi-partite setting.Keywords
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