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Quantum coding with finite resources

Author

Listed:
  • Marco Tomamichel

    (School of Physics, University of Sydney)

  • Mario Berta

    (Institute for Quantum Information and Matter, Mathematics and Astronomy, California Institute of Technology)

  • Joseph M. Renes

    (Institute for Theoretical Physics, ETH Zurich)

Abstract

The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances.

Suggested Citation

  • Marco Tomamichel & Mario Berta & Joseph M. Renes, 2016. "Quantum coding with finite resources," Nature Communications, Nature, vol. 7(1), pages 1-8, September.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms11419
    DOI: 10.1038/ncomms11419
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