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Quantum communication with Gaussian channels of zero quantum capacity


As with classical information1,2, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels3,4,5. In contrast to classical theory, imperfect quantum channels exhibit a strong kind of synergy: pairs of discrete memoryless quantum channels exist, each of zero quantum capacity, which acquire positive quantum capacity when used together6. Here, we show that this ‘superactivation’ phenomenon also occurs in the more realistic setting of optical channels with attenuation and Gaussian noise7,8. This paves the way for its experimental realization and application in real-world communications systems.

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Figure 1: Symplectic extensions of Gaussian channels.
Figure 2: A family of examples.
Figure 3: Superactivation for a wide range of parameters.
Figure 4: Generating the Hamiltonian.


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The authors thank J. Eisert and M.M. Wolf for helpful advice in the early stages of this work and C.H. Bennett for many useful suggestions. G.S. and J.Y. are especially grateful to the Institut Mittag-Leffler, where some of this work was performed, for their hospitality. J.Y.'s research was supported by grants through the Laboratory Directed Research and Development programme of the US Department of Energy. G.S. and J.A.S. were supported by the Defense Advanced Research Projects Agency (QUEST contract HR0011-09-C-0047).

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G.S., J.A.S. and J.Y. designed the research, carried out the research, and wrote the manuscript.

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Correspondence to Graeme Smith.

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The authors declare no competing financial interests.

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Smith, G., Smolin, J. & Yard, J. Quantum communication with Gaussian channels of zero quantum capacity. Nature Photon 5, 624–627 (2011).

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