Advertisement

Self-Testing Graph States

  • Matthew McKagueEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6745)

Abstract

We give a construction for a self-test for any connected graph state. In other words, for each connected graph state we give a set of non-local correlations that can only be achieved (quantumly) by that particular graph state and certain local measurements. The number of correlations considered is small, being linear in the number of vertices in the graph. We also prove robustness for the test.

Notes

Acknowledgments

This work is funded by the Centre for Quantum Technologies, which is funded by the Singapore Ministry of Education and the Singapore National Research Foundation.

References

  1. [Die10]
    Diestel, R.: Graph theory. In: Graduate Texts in Mathematics, vol. 173, 4th edn. Springer, Heidelberg. http://diestel-graph-theory.com/ (2010)
  2. [MM11]
    McKague, M., Mosca, M.: Generalized self-testing and the security of the 6-state protocol. In: van Dam, W., Kendon, V.M., Severini, S. (eds.) TQC 2010. LNCS, vol. 6519, pp. 113–130. Springer, Heidelberg (2011)Google Scholar
  3. [MMMO06]
    Magniez, F., Mayers, D., Mosca, M., Ollivier, H.: Self-testing of quantum circuits. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 72–83. Springer, Heidelberg (2006)Google Scholar
  4. [MY04]
    Mayers, D., Yao, A.: Self testing quantum apparatus. Quantum Inf. Comput. 4(4), 273–286 (2004). (http://arxiv.org/abs/quant-ph/0307205, http://www.rintonpress.com/journals/qiconline.html#v4n4)zbMATHMathSciNetGoogle Scholar
  5. [PAM+10]
    Pironio, S., Acin, A., Massar, S., Boyer de la Giroday, A., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by bell’s theorem. Nature 464(7291), 1021–1024 (2010). doi: 10.1038/nature09008. (EPRINT aXiv:0911.3427)CrossRefGoogle Scholar
  6. [RB01]
    Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86(22), 5188–5191 (2001). doi: 10.1103/PhysRevLett.86.5188. (EPRINT arxiv:quant-ph/0010033)Google Scholar
  7. [vMMS00]
    van Dam, W., Magniez, F., Mosca, M., Santha, M.: Self-testing of universal and fault-tolerant sets of quantum gates. In: STOC ’00: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 688–696. ACM, New York. (2000). doi: 10.1145/335305.335402. (EPRINT arxiv:quant-ph/9904108)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore

Personalised recommendations