Quantum Communication Complexity with Coherent States and Linear Optics

Authors Juan Miguel Arrazola, Norbert Lütkenhaus



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Juan Miguel Arrazola
Norbert Lütkenhaus

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Juan Miguel Arrazola and Norbert Lütkenhaus. Quantum Communication Complexity with Coherent States and Linear Optics. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 36-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.TQC.2014.36

Abstract

We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming a wide class of protocols in quantum communication into a form in which they can be implemented with current technology. In particular, we apply the mapping to quantum communication complexity, providing general conditions under which quantum protocols can be implemented with coherent states and linear optics while retaining exponential separations in communication complexity compared to the classical case. Finally, we make use of our results to construct a protocol for the Hidden Matching problem that retains the known exponential gap between quantum and classical one-way communication complexity.
Keywords
  • Quantum Communication Complexity
  • Quantum Optics

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References

  1. Juan Miguel Arrazola and Norbert Lütkenhaus. Quantum fingerprinting with coherent states and a constant mean number of photons. Phys. Rev. A, 89:062305, Jun 2014. Google Scholar
  2. Ziv Bar-Yossef, T. S. Jayram, and Iordanis Kerenidis. Exponential separation of quantum and classical one-way communication complexity. In STOC, pages 128-137, 2004. Google Scholar
  3. Andrew D Barbour, Lars Holst, and Svante Janson. Poisson approximation. Clarendon press Oxford, 1992. Google Scholar
  4. C. H. Bennett. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett., 68(21):3121-3124, may 1992. Google Scholar
  5. C. H. Bennett and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, pages 175-179, New York, dec 1984. IEEE. Google Scholar
  6. Gilles Brassard. Quantum communication complexity. Foundations of Physics, 33(11):1593-1616, 2003. Google Scholar
  7. Harry Buhrman, Richard Cleve, Serge Massar, and Ronald de Wolf. Nonlocality and communication complexity. Rev. Mod. Phys., 82:665-698, Mar 2010. Google Scholar
  8. Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf. Quantum fingerprinting. Phys. Rev. Lett., 87:167902, Sep 2001. Google Scholar
  9. Harry Buhrman, Richard Cleve, and Avi Wigderson. Quantum vs. classical communication and computation. In STOC, pages 63-68, 1998. Google Scholar
  10. John M. Donohue, Megan Agnew, Jonathan Lavoie, and Kevin J. Resch. Coherent ultrafast measurement of time-bin encoded photons. Phys. Rev. Lett., 111:153602, Oct 2013. Google Scholar
  11. Massimo Franceschetti, Olivier Dousse, David Tse, and Patrick Thiran. Closing the gap in the capacity of wireless networks via percolation theory. Information Theory, IEEE Transactions on, 53(3):1009-1018, 2007. Google Scholar
  12. Dmitry Gavinsky. Classical interaction cannot replace a quantum message. In STOC, pages 95-102, 2008. Google Scholar
  13. Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum metrology. Physical review letters, 96(1):010401, 2006. Google Scholar
  14. Nicolas Gisin and Rob Thew. Quantum communication. Nature Photonics, 1(3):165-171, 2007. Google Scholar
  15. Alexander Semenovich Holevo. Bounds for the quantity of information transmitted by a quantum communication channel. Problemy Peredachi Informatsii, 9(3):3-11, 1973. Google Scholar
  16. Rolf T. Horn, S. A. Babichev, Karl-Peter Marzlin, A. I. Lvovsky, and Barry C. Sanders. Single-qubit optical quantum fingerprinting. Phys. Rev. Lett., 95:150502, Oct 2005. Google Scholar
  17. Peter C. Humphreys, Benjamin J. Metcalf, Justin B. Spring, Merritt Moore, Xian-Min Jin, Marco Barbieri, W. Steven Kolthammer, and Ian A. Walmsley. Linear optical quantum computing in a single spatial mode. Phys. Rev. Lett., 111:150501, Oct 2013. Google Scholar
  18. Thaddeus D Ladd, Fedor Jelezko, Raymond Laflamme, Yasunobu Nakamura, Christopher Monroe, and Jeremy L O’Brien. Quantum computers. Nature, 464(7285):45-53, 2010. Google Scholar
  19. Ran Raz. Exponential separation of quantum and classical communication complexity. In STOC, pages 358-367, 1999. Google Scholar
  20. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani. Experimental realization of any discrete unitary operator. Phys. Rev. Lett., 73:58-61, 1994. Google Scholar
  21. M Sasaki, M Fujiwara, H Ishizuka, W Klaus, K Wakui, M Takeoka, S Miki, T Yamashita, Z Wang, A Tanaka, et al. Field test of quantum key distribution in the tokyo qkd network. Optics Express, 19(11):10387-10409, 2011. Google Scholar
  22. Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J Cerf, Miloslav Dušek, Norbert Lütkenhaus, and Momtchil Peev. The security of practical quantum key distribution. Reviews of modern physics, 81(3):1301, 2009. Google Scholar
  23. R. Sheldon. A First Course In Probability, 6/E. Pearson Education, 2002. Google Scholar
  24. Damien Stucki, Nino Walenta, Fabien Vannel, Robert Thomas Thew, Nicolas Gisin, Hugo Zbinden, S Gray, CR Towery, and S Ten. High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres. New Journal of Physics, 11(7):075003, 2009. Google Scholar
  25. Sébastien Tanzilli, Anthony Martin, Florian Kaiser, Marc P De Micheli, Olivier Alibart, and Daniel B Ostrowsky. On the genesis and evolution of integrated quantum optics. Laser & Photonics Reviews, 6(1):115-143, 2012. Google Scholar
  26. Pavel Trojek, Christian Schmid, Mohamed Bourennane, \ifmmode \checkC\else Č\fiaslav Brukner, Marek \ifmmode \dotZ\else Ż\fiukowski, and Harald Weinfurter. Experimental quantum communication complexity. Phys. Rev. A, 72:050305, Nov 2005. Google Scholar
  27. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In STOC, pages 209-213, 1979. Google Scholar
  28. Jun Zhang, Xiao-Hui Bao, Teng-Yun Chen, Tao Yang, Adán Cabello, and Jian-Wei Pan. Experimental quantum "guess my number" protocol using multiphoton entanglement. Phys. Rev. A, 75:022302, Feb 2007. Google Scholar
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