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Foundations of Physics

, Volume 46, Issue 5, pp 620–634 | Cite as

Communication Strength of Correlations Violating Monogamy Relations

  • Waldemar Kłobus
  • Michał Oszmaniec
  • Remigiusz Augusiak
  • Andrzej Grudka
Article

Abstract

In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this aim, we first provide a framework associating them with classical channels whose capacities are then used to quantify the usefulness of these correlations in sending information. Finally, we determine the minimal amount of information that can be sent using signaling correlations violating the monogamy relation associated to the chained Bell inequalities.

Keywords

Monogamy relations No-signaling principle Capacities of communication channels 

Notes

Acknowledgments

We thank M. Horodecki, R. Horodecki, P. Kurzyński, M. Lewenstein, J. Łodyga and A. Wójcik for helpful discussions. W. K. and A. G. were supported by the Polish Ministry of Science and Higher Education Grant no. IdP2011 000361. M. O. was supported by the ERC Advanced Grant QOLAPS, START scholarship granted by Foundation for Polish Science, the Polish National Science Centre grant under Contract No. DEC-2011/01/M/ST2/00379, the John Templeton Foundation, the Spanish MINECO grant FOQUS, the “Severo Ochoa” Programme (SEV-2015-0522), and the Generalitat de Catalunya grant SGR875. R. A. was supported by the ERC Advanced Grant OSYRIS, the EU IP SIQS, the John Templeton Foundation, the Spanish Ministry project FOQUS (FIS2013-46768) and the Generalitat de Catalunya project 2014 SGR 874. W. K. thanks the Foundation of Adam Mickiewicz University in Poznań for the support from its scholarship programme. A.G. thanks ICFO–Institut de Ciències Fotòniques for hospitality.

References

  1. 1.
    Masanes, L., Acín, A., Gisin, N.: General properties of nonsignaling theories. Phys. Rev. A 73, 012112 (2006)ADSCrossRefGoogle Scholar
  2. 2.
    Barrett, J.: Information processing in generalized probabilistic theories. Phys. Rev. A 75, 032304 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379 (1994)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Pawłowski, M., Paterek, T., Kaszlikowski, D., Scarani, V., Winter, A., Żukowski, M.: Information causality as a physical principle. Nature 461, 1101 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    Navascués, M., Wunderlich, H.: A glance beyond the quantum model. Proc. Roy. Soc. A 466, 881 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fritz, T., Sainz, A.B., Augusiak, R., Brask, J.B., Chaves, R., Leverrier, A., Acín, A.: Local orthogonality as a multipartite principle for quantum correlations. Nat. Commun. 4, 2263 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    Navascués, M., Guryanova, Y., Hoban, M.J., Acín, A.: Almost quantum correlations. Nat. Commun. 6, 6288 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    Toner, B.: Monogamy of non-local quantum correlations. Proc. R. Soc. A 465, 59 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Pawłowski, M., Brukner, C.: Monogamy of Bells inequality violations in nonsignaling theories. Phys. Rev. Lett. 102, 030403 (2009)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Augusiak, R., Demianowicz, M., Pawłowski, M., Tura, J., Acín, A.: Elemental and tight monogamy relations in nonsignaling theories. Phys. Rev. A 90, 052323 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    Ramanathan, R., Horodecki, P.: Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities. Phys. Rev. Lett. 113, 210403 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)ADSCrossRefGoogle Scholar
  14. 14.
    Braunstein, S.L., Caves, C.M.: Wringing out better Bell inequalities. Ann. Phys. 202, 22 (1990)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Barrett, J., Hardy, L., Kent, A.: No signaling and quantum key distribution. Phys. Rev. Lett 95, 010503 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Colbeck, R., Renner, R.: Free randomness can be amplified. Nat. Phys. 8, 450 (2012)CrossRefGoogle Scholar
  17. 17.
    Gallego, R., Masanes, L., de la Torre, G., Dhara, C., Aolita, L., Acín, A.: Full randomness from arbitrarily deterministic events. Nat. Commun. 4, 2654 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    Brandão, F.G.S.L., Ramanathan, R., Grudka, A., Horodecki, K., Horodecki, M., Horodecki, P.: Robust device-independent randomness amplification with few devices. arXiv:1310.4544
  19. 19.
    Almheiri, A., Marolf, D., Polchinski, J., Sully, J.: Black holes: complementarity or firewalls? JHEP 02, 062 (2013)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Oppenheim, J., Unruh, B.: Firewalls and flat mirrors: an alternative to the AMPS experiment which evades the Harlow-Hayden obstacle. JHEP 03, 120 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Preskill, J., Lloyd, S.: Unitarity of black hole evaporation in final-state projection models, JHEP 08, 126 (2014)Google Scholar
  22. 22.
    Grudka, A., Hall, M.J.W., Horodecki, M., Horodecki, R., Oppenheim, J., Smolin, J.: arXiv:1506.07133
  23. 23.
    Horowitz, G.T., Maldacena, J.: The black hole final state. JHEP 02, 008 (2004)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Moser, S.M.: Error probability analysis of binary asymmetric channels, final report of NSC project ‘Finite Blocklength Capacity’, http://moser-isi.ethz.ch/docs/papers/smos-2012-4.pdf
  25. 25.
    Shannon, C.E.: Collected Papers. Wiley-IEEE Press, New York (1993)zbMATHGoogle Scholar
  26. 26.
    Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Waldemar Kłobus
    • 1
  • Michał Oszmaniec
    • 2
    • 3
  • Remigiusz Augusiak
    • 2
    • 3
  • Andrzej Grudka
    • 1
  1. 1.Faculty of PhysicsAdam Mickiewicz UniversityPoznańPoland
  2. 2.ICFO–Institut de Ciencies FotoniquesCastelldefels (Barcelona)Spain
  3. 3.Center for Theoretical PhysicsPolish Academy of SciencesWarszawaPoland

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