Gaussian quantum information theory, the entanglement of formation and the logarithmic negativity [10] — but, of course, this does not imply that no such equation can exist. 

Addendum: Right after completion of this work, Wang et al. [11] indeed published a Gaussian entanglement evo- lution equation using a different entanglement measure which is introduced in their article. This entanglement measure is a non-standard entanglement of formation based upon the shortest distance measure for pure states. Against the background of our numerical nogo results for a potential, quantitative entanglement evolution equa- tion using the standard entanglement of formation [10], the results of ref. [11] based on a non-standard entangle- ment of formation are very surprising. 

We thank Raffaele Romano for very valuable discus- sions. J.H. acknowledges support through the BayBFG and the Studienstiftung des deutschen Volkes. P.v.L. ac- knowledges the DFG for financial support through the Emmy Noether programme. 

∗ Electronic address: peter.vanloock@mpl.mpg.de 

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[13] Local quantum channels also play a very important role in quantum communication because they include the lossy and noisy fiber channels which come up in the con- text of entanglement distribution. 

[14] The use of the concurrence is essential because the proof of (2) relies on the analytic formula for the concurrence of arbitrary (pure and mixed) two-qubit states [12]. 

[15] For example, continuous variable implementations are usually deterministic while qubit protocols are often probabilistic. See, for example, [4] for a recent review of continuous variable quantum information processing. 

[16] This is particularly counterintuitive since the entangle- ment of Gaussian states is unbounded. Hence, the entan- glement of the state Y can be arbitrarily high. 

