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Limits on classical communication from quantum entropy power inequalities

An Erratum to this article was published on 27 February 2013

This article has been updated


Almost all modern communication systems rely on electromagnetic fields. The additive white Gaussian noise (AWGN) channel is often a good approximate description of such a system, and its information-carrying capacity is given by a simple formula. The quantum analogue of AWGN channels, the bosonic Gaussian noise channel, accurately describes many quantum optical communication systems of interest. Estimating its capacity is significantly more difficult; although some simple coding strategies are known, whether or not more sophisticated techniques could dramatically improve communication rates has been unknown. Here, we present strong new upper bounds for the classical capacity of bosonic Gaussian noise channels. These results imply that known coding techniques are typically close to optimal. Our main technical tool is an entropy power inequality bounding the entropy produced as two quantum signals combine at a beamsplitter. Its proof relies on a quantum diffusion process which smooths arbitrary states towards Gaussians.

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Figure 1: Two independent quantum signals combined at a beamsplitter.
Figure 2: An additive noise channel arises when an input signal A interacts via a beamsplitter with initial environment Ein followed by a partial trace over Eout resulting in an output signal B.
Figure 3: Known bounds on the classical capacity of thermal noise channels.
Figure 4: Using the evolution of the inputs and output of a beamsplitter under diffusion to prove the quantum entropy power inequality.

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  • 24 January 2013

    In the version of this Article originally published, the author affiliations were incorrect and should have read: 1IBM TJ Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, New York 10598, USA, 2Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, ON, Canada, N2L3G1. This has now been corrected in the HTML and PDF versions of the Article.


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The authors thank C. Bennett, J. Gambetta and J. Smolin for helpful comments and S. Guha for discussions. Both authors were supported by the Defense Advance Research Projects Agency Quantum Entanglement Science and Technology programme (contract no. HR0011-09-C-0047).

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R.K. and G.S. designed and carried out the research and wrote the paper.

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Correspondence to Robert König or Graeme Smith.

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König, R., Smith, G. Limits on classical communication from quantum entropy power inequalities. Nature Photon 7, 142–146 (2013).

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