Skip to main content
Log in

Experimental multipartner quantum communication complexity employing just one qubit

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

Most proposals for quantum solutions of information-theoretic problems rely on the usage of multi-partite entangled states which are still difficult to produce experimentally with current state-of-the-art technology. Here, we analyze a scheme to simplify a particular kind of multiparty communication protocols for the experiment. We prove that the fidelity of two communication complexity protocols, allowing for an N − 1 bit communication, can be exponentially improved by N − 1 (unentangled) qubit communication. Taking into account, for a fair comparison, all inefficiencies of state-of-the-art set-up, the experimental implementation for N = 5 outperforms the best classical protocol, making it the candidate for multi-party quantum communication applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Bennett CH, Brassard G (1984) Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International conference on computers, systems and signal processing. IEEE, New York, p 175–179

  • Brukner Č, Żukowski M, Pan J-W, Zeilinger A (2004) Bell’s inequalities and quantum communication complexity. Phys Rev Lett 92:127901

    Article  MathSciNet  Google Scholar 

  • Brukner Č, Żukowski M, Zeilinger A (2002) Quantum communication complexity protocol with two entangled qutrits. Phys Rev Lett 89:197901

    Article  Google Scholar 

  • Buhrman H, Cleve R, van Dam W (2001) Quantum entanglement and communication complexity. Siam J Comput 30:1829–1841; [e-print: quant-ph/9705033]

    Google Scholar 

  • Buhrman H, Cleve R, Wigderson A (1998) Quantum vs. classical communication and computation. In: Proceedings of the 30th annual ACM symposium on theory of computing. ACM Press, New York, p 63–68

  • Buhrman H, van Dam W, Høyer P, Tapp A (1999) Multiparty quantum communication complexity. Phys Rev A 60:2737–2741

    Article  Google Scholar 

  • Cabello A, López-Tarrida J (2005) Proposed experiment for the quantum “Guess My Number” protocol. Phys Rev A 71:020301(R)

    Article  Google Scholar 

  • Cleve R, van Dam W, Nielsen M, Tapp A (1999) Quantum entanglement and the communication complexity of the inner product function. Lecture notes in computer science, vol. 1509. Springer, London, p 61–74

  • Cleve R, Gottesmann D, Lo H-K (1999) How to share a quantum secret. Phys Rev Lett 83:648

    Article  Google Scholar 

  • Ekert AK (1991) Quantum cryptography based on Bell’s theorem. Phys Rev Lett 67:661

    Article  MathSciNet  MATH  Google Scholar 

  • Gaertner S, Kurtsiefer C, Bourennane M, Weinfurter H (2007) Experimental demonstration of four-party quantum secret sharing. Phys Rev Lett 98:020503

    Article  Google Scholar 

  • Galvão EF (2002) Feasible quantum communication complexity protocol. Phys Rev A 65:012318

    Article  Google Scholar 

  • Gisin N, Ribordy G, Tittel W, Zbinden H (2002) Quantum cryptography. Rev Mod Phys 74:145

    Article  Google Scholar 

  • Hardy L, van Dam W (1999) Quantum communication using a nonlocal Zeno effect. Phys Rev A 59:2635–2640

    Article  MathSciNet  Google Scholar 

  • Hillery M, Bužek V, Berthiaume A (1999) Quantum secret sharing. Phys Rev A 59:1829

    Article  MathSciNet  Google Scholar 

  • Holevo AS Bounds for the quantity of information transmitted by a quantum communication channel. Probl Peredachi Inf 9:3–11 (1973) [transl: Probl Inf Transm 9:177–183 (1973)]

  • Horn RT, Babichev SA, Marzlin K-P, Lvovsky AI, Sanders BC (2005) Single-qubt optical quantum fingerprinting. Phys Rev Lett 95:150502

    Article  Google Scholar 

  • Karlsson A, Koashi M, Imoto N (1998) Quantum entanglement for secret sharing and secret splitting. Phys Rev A 59:162

    Article  Google Scholar 

  • Kushilevitz E, Nisan N (1997) Communication complexity. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Raz R (1999) Exponential separation of quantum and classical communication complexity. In: Proceedings of the 31th annual ACM symposium on theory of computing. ACM Press, New York, pp 358–367

  • Schmid C, Trojek P, Bourennane M, Kurtsiefer C, Żukowski M, Weinfurter H (2005) Experimental single qubit quantum secret sharing. Phys Rev Lett 95:230505

    Article  Google Scholar 

  • Trojek P, Schmid C, Bourennane M, Brukner Č, Żukowski M, Weinfurter H (2005) Experimental quantum communication complexity. Phys Rev A 72:050305(R)

    Article  Google Scholar 

  • Xue P, Huang Y-F, Zhang Y-S, Li C-F, Guo G-C (2001) Reducing the communication complexity with quantum entanglement. Phys Rev A 64:032304

    Article  Google Scholar 

  • Yao AC-C (1979) Some complexity questions related to distributed computing. In: Proceedings of the 11th annual ACM symposium on theory of computing. ACM Press, New York, pp 209–213

  • Zhang J, Bao X-H, Chen T-Y, Yang T, Cabello A, Pan J-W (2007) Experimental quantum “Guess my Number” protocol using multiphoton entanglement. Phys Rev A 75:022302

    Article  Google Scholar 

  • Żukowski M (1993) Bell theorem involving all settings of measuring apparatus. Phys Lett A 177:290–296

    Article  MathSciNet  Google Scholar 

  • Żukowski M, Zeilinger A, Horne MA, Weinfurter H (1998) Quest for GHZ states. Acta Phys Pol 93:187

    Google Scholar 

Download references

Acknowledgements

This work was supported by the DFG, EU-FET (RamboQ, IST-2001-38864), Marie-Curie program and DAAD/KBN exchange program. M.Ż. was supported by the VI Framewoerk EU programmes QAP and SCALA as well as by Wenner Gren Foundations.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pavel Trojek.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Trojek, P., Schmid, C., Bourennane, M. et al. Experimental multipartner quantum communication complexity employing just one qubit. Nat Comput 12, 19–26 (2013). https://doi.org/10.1007/s11047-012-9352-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-012-9352-7

Keywords

Navigation