Article

Limitations on quantum key repeaters

  • Nature Communications 6, Article number: 6908 (2015)
  • doi:10.1038/ncomms7908
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Abstract

A major application of quantum communication is the distribution of entangled particles for use in quantum key distribution. Owing to noise in the communication line, quantum key distribution is, in practice, limited to a distance of a few hundred kilometres, and can only be extended to longer distances by use of a quantum repeater, a device that performs entanglement distillation and quantum teleportation. The existence of noisy entangled states that are undistillable but nevertheless useful for quantum key distribution raises the question of the feasibility of a quantum key repeater, which would work beyond the limits of entanglement distillation, hence possibly tolerating higher noise levels than existing protocols. Here we exhibit fundamental limits on such a device in the form of bounds on the rate at which it may extract secure key. As a consequence, we give examples of states suitable for quantum key distribution but unsuitable for the most general quantum key repeater protocol.

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Acknowledgements

Part of this work was done when the authors attended the programme ‘Mathematical Challenges in Quantum Information’, August–December 2013, at the Isaac Newton Institute for Mathematical Sciences, Cambridge, whose hospitality is gratefully acknowledged. M.C. was with ETH Zurich and visiting the Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, during part of this work. We thank Gláucia Murta for pointing out an error in an earlier version of the manuscript. K.H. thanks Michał and Paweł Horodecki and Jonathan Oppenheim for helpful discussions. M.C. was supported by a DFF Sapere Aude grant, an ERC Starting Grant, the CHIST-ERA project ‘CQC’, an SNSF Professorship, the Swiss NCCR ‘QSIT’ and the Swiss SBFI in relation to COST action MP1006. K.H. acknowledges support by the ERC Advanced Grant ‘QOLAPS’ and the National Science Centre project Maestro DEC-2011/02/A/ST2/00305. A.W. was supported by the Spanish MINECO, projects FIS2013-40627-P and FIS2008-01236 with the support of FEDER funds, the Generalitat de Catalunya CIRIT project 2014 SGR 966, the EC STREP ‘RAQUEL’ and the Philip Leverhulme Trust. A.W. and S.B. were supported by the ERC Advanced Grant ‘IRQUAT’.

Author information

Affiliations

  1. Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK

    • Stefan Bäuml
    •  & Andreas Winter
  2. Fisica Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain

    • Stefan Bäuml
    •  & Andreas Winter
  3. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark

    • Matthias Christandl
  4. Institute of Informatics, University of Gdańsk, 80-952 Gdańsk, Poland

    • Karol Horodecki
  5. National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland

    • Karol Horodecki
  6. ICREA—Institució Catalana de Recerca i Estudis Avançats, ES-08010 Barcelona, Spain

    • Andreas Winter

Authors

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Contributions

All authors contributed to defining the formalism and to obtaining the main results of the paper. M.C. and K.H. focused on the distinguishability bound, S.B. and A.W. on bounding the entanglement of the output state.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Stefan Bäuml.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Notes 1-6 and Supplementary References

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