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Quantum Key Distribution

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Quantum Information and Coherence

Part of the book series: Scottish Graduate Series ((SGS))

Abstract

Quantum Key Distribution (QKD) is the first practical application of the field of quantum information science that reached the commercial market. Here the basics principles of QKD are laid out. We discuss not only abstract concepts, but also make the connection to actual optical implementation of basic protocols.

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Notes

  1. 1.

    Note that error free decoding does not imply data integrity. As Eve is in control of the cryptogram \(C\), she might modify it to \(C'\) which Bob might decode to message \(M'\) without any warning flags.

  2. 2.

    One example of signal states with this property will be the BB84 signals.

  3. 3.

    The term ‘Generating Non-orthogonal’ is not a standard term, and I am still looking for a more suitable name!

  4. 4.

    Note that any channel can be written as Completely Positive Trace Preserving Map from system \(A'\) to \(B\), which in turn can be represented as a unitary mapping the combined systems \((A',E')\) to \((B,E)\) by using sufficiently large and proper dimensioned systems \(E'\) and \(E\).

  5. 5.

    Note that often we know that the error rate is due to misalignment and dark counts in our detectors, but for a security analysis we have to work with the worst-case scenario that all observed imperfections are due to Eve. If one can guarantee somehow that the imperfections are out of Eve’s control, then one can in principle take account of this in the security proofs. However, it turns out that it is not easy to give convincing arguments that something is outside of Eve’s control, and moreover, the resulting security analysis will become technically much harder.

  6. 6.

    Actually, it is possible to separate the success of error correction from the other properties.

  7. 7.

    Note that there are QKD protocols which use the same signals states and measurements as in the BB84 protocol but a different post-processing route, resulting in an increased error threshold.

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Authors and Affiliations

  1. Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada

    Norbert Lütkenhaus

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  1. Norbert Lütkenhaus
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Correspondence to Norbert Lütkenhaus .

Editor information

Editors and Affiliations

  1. Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, United Kingdom

    Erika Andersson

  2. Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, United Kingdom

    Patrik Öhberg

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© 2014 Norbert Lutkenhaus

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Lütkenhaus, N. (2014). Quantum Key Distribution. In: Andersson, E., Öhberg, P. (eds) Quantum Information and Coherence. Scottish Graduate Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04063-9_5

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