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Unbounded number of channel uses may be required to detect quantum capacity

Author

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  • Toby Cubitt

    (University of Cambridge)

  • David Elkouss

    (Universidad Complutense de Madrid)

  • William Matthews

    (University of Cambridge
    Statistical Laboratory, University of Cambridge)

  • Maris Ozols

    (University of Cambridge)

  • David Pérez-García

    (Universidad Complutense de Madrid)

  • Sergii Strelchuk

    (University of Cambridge)

Abstract

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.

Suggested Citation

  • Toby Cubitt & David Elkouss & William Matthews & Maris Ozols & David Pérez-García & Sergii Strelchuk, 2015. "Unbounded number of channel uses may be required to detect quantum capacity," Nature Communications, Nature, vol. 6(1), pages 1-4, November.
    • Handle: RePEc:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms7739
    DOI: 10.1038/ncomms7739
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