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Exact solution for the quantum and private capacities of bosonic dephasing channels

Nature Photonics volume 17, pages 525–530 (2023)Cite this article

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Abstract

The capacities of noisy quantum channels capture the ultimate rates of information transmission across quantum communication lines, and the quantum capacity plays a key role in determining the overhead of fault-tolerant quantum computation platforms. Closed formulae for these capacities in bosonic systems were lacking for a key class of non-Gaussian channels, bosonic dephasing channels, which are used to model noise affecting superconducting circuits and fibre-optic communication channels. Here we provide an exact calculation of the quantum, private, two-way assisted quantum and secret-key-agreement capacities of all bosonic dephasing channels. We prove that they are equal to the relative entropy of the distribution underlying the channel with respect to the uniform distribution, solving a problem that was originally posed over a decade ago.

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Fig. 1: A depiction of a quantum communication protocol that uses the channel \({{{\mathcal{N}}}}\) a total of n times to send a quantum system M reliably.
Fig. 2: An LOCC-assisted protocol that involves n uses of the quantum channel \({{{\mathcal{N}}}}\), assumed to connect two spatially separated laboratories belonging to Alice and Bob.
Fig. 3: The capacities of the BDCs associated with the wrapped normal distribution (pγ), the von Mises distribution (pλ) and the wrapped Cauchy distribution (pκ).

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Acknowledgements

We thank S. Mancini for discussions. L.L. was partially supported by the Alexander von Humboldt Foundation. M.M.W. acknowledges support from the National Science Foundation under grant no. 2014010.

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Authors and Affiliations

  1. Institut für Theoretische Physik und IQST, Universität Ulm, Ulm, Germany

    Ludovico Lami

  2. QuSoft, Amsterdam, The Netherlands

    Ludovico Lami

  3. Korteweg–de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands

    Ludovico Lami

  4. Institute for Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands

    Ludovico Lami

  5. Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA

    Mark M. Wilde

  6. School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA

    Mark M. Wilde

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  1. Ludovico Lami
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Correspondence to Ludovico Lami or Mark M. Wilde.

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Supplementary Sections 1–4, Figs. 1–3, refs. 1–75 and detailed mathematical derivations of claims made in the text.

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Lami, L., Wilde, M.M. Exact solution for the quantum and private capacities of bosonic dephasing channels. Nat. Photon. 17, 525–530 (2023). https://doi.org/10.1038/s41566-023-01190-4

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