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Ultimate classical communication rates of quantum optical channels


Optical channels, such as fibres or free-space links, are ubiquitous in today's telecommunication networks. They rely on the electromagnetic field associated with photons to carry information from one point to another in space. A complete physical model of these channels must necessarily take quantum effects into account to determine their ultimate performances. Single-mode, phase-insensitive bosonic Gaussian channels have been extensively studied over past decades, given their importance for practical applications. In spite of this, a long-standing unsolved conjecture on the optimality of Gaussian encodings has prevented finding their classical communication capacity. Here, this conjecture is solved by proving that the vacuum state achieves the minimum output entropy of these channels. This establishes the ultimate achievable bit rate under an energy constraint, as well as the long awaited proof that the single-letter classical capacity of these channels is additive.

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Figure 1: Compact representation of single-mode phase-insensitive channels.
Figure 2: Plots of the capacities and minimal output entropies for thermal , classical additive noise , amplifier and contravariant amplifier BGCs.
Figure 3: Graphical representation of equation (6).


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The authors thank L. Ambrosio, A. Mari, C. Navarrete-Benloch, J. Oppenheim, M.E. Shirokov, R.F. Werner and A. Winter for comments and discussions. The authors acknowledge support and the catalysing role of the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; an important part of this work was conducted when attending the Newton Institute programme ‘Mathematical Challenges in Quantum Information’. A.H. acknowledges the Rothschild Distinguished Visiting Fellowship, which enabled him to participate in the programme, and partial support from RAS Fundamental Research Programs (the Russian Quantum Center). N.J.C. and R.G.-P. acknowledge financial support from the Belgian Fonds de la Recherche Scientifique (F.R.S.–FNRS) under projects T.0199.13 and HIPERCOM (High-Performance Coherent Quantum Communications), as well as from the ‘Interuniversity Attraction Poles’ programme of the Belgian Science Policy Office (grant no. IAP P7-35 Photonics@be). R.G.-P. acknowledges financial support from the Alexander von Humboldt Foundation, the F.R.S.–FNRS and Back-to-Belgium grant from the Belgian Federal Science Policy.

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Correspondence to V. Giovannetti.

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Giovannetti, V., García-Patrón, R., Cerf, N. et al. Ultimate classical communication rates of quantum optical channels. Nature Photon 8, 796–800 (2014).

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