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Standard super-activation for Gaussian channels requires squeezing

Daniel Lercher, Géza Giedke, Michael M. Wolf

New J. Phys. 15 123003 , (2013)

DOI: 10.1088/1367-2630/15/12/123003 Pfeil
*arXiv.org*: 1209.5574 Pfeil

Abstract: The quantum capacity of bosonic Gaussian quantum channels can be non-additive in a particularly striking way: a pair of such optical-fiber type channels can individually have zero quantum capacity but super-activate each other such that the combined channel has strictly positive capacity. This has been shown in [Nature Photonics 5, 624 (2011)] where it was conjectured that squeezing is a necessary resource for this phenomenon. We provide a proof of this conjecture by showing that for gauge covariant channels a Choi matrix with positive partial transpose implies that the channel is entanglement-breaking. In addition, we construct an example which shows that this implication fails to hold for Gaussian channels which arise from passive interactions with a squeezed environment.