Theory of channel simulation and bounds for private communication

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We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of several fundamental channels, including the bosonic lossy channel. We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein-Kimble teleportation protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution.
Original languageEnglish
Article number035009
JournalQuantum Sci. Technol.
Issue number3
Publication statusPublished - 31 May 2018

Bibliographical note

Review paper which also contains new results. Revised version. REVTeX. 28 pages. 2 tables and 4 figures.
This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details


  • quant-ph
  • cond-mat.other
  • math-ph
  • math.MP
  • physics.optics
  • quantum teleportation
  • quantum cryptography
  • entanglement
  • quantum channels
  • quantum capacities
  • Gaussian channels

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