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Witnessing Causal Nonseparability: Theory and Experiment

  • Christina GiarmatziEmail author
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

We develop a technique to witness a process that is not causally separable, in that it cannot be written as a fixed-order quantum circuit or a mixture of those. Using the process matrix formalism, we find a set of measurements within the process that proves causal non-separability. The problem of finding these measurements can be written as a SemiDefinite Program that can be solved efficiently. We apply our method in an experiment we performed in our labs, where we implemented a causally non-separable process and proved it to be so by performing unitary operations and final measurements.

References

  1. 1.
    Araújo M et al (2015) Witnessing causal nonseparability. New J Phys 17:102001CrossRefGoogle Scholar
  2. 2.
    Oreshkov O, Costa F, Brukner Č (2012) Quantum correlations with no causal order. Nat Commun 3:1092ADSCrossRefGoogle Scholar
  3. 3.
    Oreshkov O, Giarmatzi C (2016) Causal and causally separable processes. New J Phys 18:093020CrossRefGoogle Scholar
  4. 4.
    Hardy L (2009) Foliable operational structures for general probabilistic theories. In: Halvorson H (ed) Deep beauty: understanding the quantum world through mathematical innovation, p 409Google Scholar
  5. 5.
    Coecke B (2010) Quantum picturalism. Contemp Phys 51:59–83ADSCrossRefGoogle Scholar
  6. 6.
    Chiribella G, D’Ariano GM, Perinotti P (2010) Probabilistic theories with purification. Phys Rev A 81:062348ADSCrossRefGoogle Scholar
  7. 7.
    Chiribella G, D’Ariano GM, Perinotti P (2011) Informational derivation of quantum theory. Phys Rev A 84:012311ADSCrossRefGoogle Scholar
  8. 8.
    Chiribella G, D’Ariano GM, Perinotti P, Valiron B (2013) Quantum computations without definite causal structure. Phys Rev A 88:022318ADSCrossRefGoogle Scholar
  9. 9.
    Chiribella G (2012) Perfect discrimination of no-signalling channels via quantum superposition of causal structures. Phys Rev A 86:040301ADSCrossRefGoogle Scholar
  10. 10.
    Araújo M, Costa F, Brukner Č (2014) Computational advantage from quantum-controlled ordering of gates. Phys Rev Lett 113:250402ADSCrossRefGoogle Scholar
  11. 11.
    Procopio LM et al (2015) Experimental superposition of orders of quantum gates. Nat Commun 6:7913Google Scholar
  12. 12.
    Rubino G et al (2017) Experimental verification of an indefinite causal order. Sci Adv 3ADSCrossRefGoogle Scholar
  13. 13.
    Rockafellar RT (1970) Convex analysis. Princeton University PressGoogle Scholar
  14. 14.
    Gutoski G, Watrous J (2006) Toward a general theory of quantum games. In: Proceedings of 39th ACM STOC, pp 565–574Google Scholar
  15. 15.
    Chiribella G, D’Ariano GM, Perinotti P (2009) Theoretical framework for quantum networks. Phys Rev A 80:022339ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Nesterov Y, Nemirovskii A (1987) Interior point polynomial algorithms in convex programming. Studies in Applied Mathematics (Society for Industrial and Applied Mathematics)Google Scholar
  17. 17.
    Goswami K et al (2018) Indefinite causal order in a quantum switch. Phys Rev Lett 121:090503Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsThe University of QueenslandBrisbaneAustralia

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