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An exactly solvable model for quantum communications

Abstract

Information theory establishes the ultimate limits on performance for noisy communication systems1. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable2,3,4,5. As a result, communication capacities—the maximum possible rates of data transmission—are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise6. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution.

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Figure 1: Phase-space representation of states (Wigner functions).
Figure 2: The DQM of the action of a channel.
Figure 3: Attenuation and thermal noise channels.
Figure 4: Multi-user channels.

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Acknowledgements

This work was supported by the DARPA QUEST programme under contract no. HR0011-09-C-0047.

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G.S. and J.A.S. designed the research and carried out the research and computations. Both authors wrote the paper.

Corresponding author

Correspondence to Graeme Smith.

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The authors declare no competing financial interests.

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Smith, G., Smolin, J. An exactly solvable model for quantum communications. Nature 504, 263–267 (2013). https://doi.org/10.1038/nature12669

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