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Quantum violation of an instrumental test


Inferring causal relations from experimental observations is of primal importance in science. Instrumental tests provide an essential tool for that aim, as they allow one to estimate causal dependencies even in the presence of unobserved common causes. In view of Bell’s theorem, which implies that quantum mechanics is incompatible with our most basic notions of causality, it is of utmost importance to understand whether and how paradigmatic causal tools obtained in a classical setting can be carried over to the quantum realm. Here we show that quantum effects imply radically different predictions in the instrumental scenario. Among other results, we show that an instrumental test can be violated by entangled quantum states. Furthermore, we demonstrate such violation using a photonic set-up with active feed-forward of information, thus providing an experimental proof of this new form of non-classical behaviour. Our findings have fundamental implications in causal inference and may also lead to new applications of quantum technologies.

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Fig. 1: DAG representation of causal structures.
Fig. 2: Experimental apparatus for the violation of the instrumental inequality.
Fig. 3: Experimental results for the violation of the instrumental inequality.


  1. Wright, P. G. et al. Tariff on Animal and Vegetable Oils (1928).

  2. Angrist, J. D., Imbens, G. W. & Rubin, D. B. Identification of causal effects using instrumental variables. J. Am. Stat. Assoc. 91, 444–455 (1996).

    Article  MATH  Google Scholar 

  3. Greenland, S. An introduction to instrumental variables for epidemiologists. Int. J. Epidemiol. 29, 722–729 (2000).

    Article  Google Scholar 

  4. Balke, A. & Pearl, J. Bounds on treatment effects from studies with imperfect compliance. J. Am. Stat. Assoc. 92, 1171–1176 (1997).

    Article  MATH  Google Scholar 

  5. Pearl, J. Causality. (Cambridge Univ. Press, Cambridge, 2009).

    Book  MATH  Google Scholar 

  6. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).

    Article  ADS  Google Scholar 

  7. Pearl, J. On the testability of causal models with latent and instrumental variables. In Proc. Eleventh Conf. on Uncertainty in Artificial Intelligence 435–443 (Morgan Kaufmann, 1995).

  8. Bell, J. S. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964).

    Article  Google Scholar 

  9. Leifer, M. S. & Spekkens, R. W. Towards a formulation of quantum theory as a causally neutral theory of bayesian inference. Phys. Rev. A 88, 052130 (2013).

    Article  ADS  Google Scholar 

  10. Fritz, T. Beyond Bell’s theorem II: Scenarios with arbitrary causal structure. Commun. Math. Phys. 341, 391–434 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Procopio, L. M. et al. Experimental superposition of orders of quantum gates. Nat. Commun. 6, 7913 (2015).

    Article  Google Scholar 

  12. Rubino, G. et al. Experimental verification of an indefinite causal order. Sci. Adv. 3 (2017),

  13. Henson, J., Lal, R. & Pusey, M. F. Theory-independent limits on correlations from generalized bayesian networks. New J. Phys. 16, 113043 (2014).

    Article  ADS  Google Scholar 

  14. Chaves, R., Majenz, C. & Gross, D. Information–theoretic implications of quantum causal structures. Nat. Comm. 6, 5766 (2015).

    Article  ADS  Google Scholar 

  15. Pienaar, J. & Brukner, C. A graph-separation theorem for quantum causal models. New J. Phys. 17, 073020 (2015).

    Article  ADS  Google Scholar 

  16. Costa, F. & Shrapnel, S. Quantum causal modelling. New J. Phys. 18, 063032 (2016).

    Article  ADS  Google Scholar 

  17. Allen, J.-M. A, Barrett, J., Horsman, D. C., Lee, C. M. & Spekkens, R. W. Quantum common causes and quantum causal models. arXiv preprint arXiv:1609.09487 (2016).

  18. Fitzsimons, J., Jones J. & Vedral, V. Quantum correlations which imply causation. arXiv preprint: 1302.2731 (2013).

  19. Ried, K. et al. A quantum advantage for inferring causal structure. Nat. Phys. 11, 414–420 (2015).

    Article  Google Scholar 

  20. MacLean, J.-P. W., Ried, K., Spekkens, R. W. & Resch, K. J. Quantum-coherent mixtures of causal relations. Nat. Comm. 8, 15149 (2017).

    Article  ADS  Google Scholar 

  21. Schafer, J. L. & Kang, J. Average causal effects from nonrandomized studies: a practical guide and simulated example. Psychol. Methods 13, 279–313 (2008).

    Article  Google Scholar 

  22. Giacomini, S., Sciarrino, F., Lombardi, E. & De Martini, F. Active teleportation of a quantum bit. Phys. Rev. A 66, 030302 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  23. Sciarrino, F., Ricci, M., De Martini, F., Filip, R. & Mista, L. Realization of a minimal disturbance quantum measurement. Phys. Rev. Lett. 96, 020408 (2006).

    Article  ADS  Google Scholar 

  24. Ringbauer, M. et al. Experimental test of nonlocal causality. Sci. Adv. 2 (2016),

  25. Boyd, S. & Vandenberghe, L. Convex Optimization. (Cambridge Univ. Press, Cambridge, 2004).

    Book  MATH  Google Scholar 

  26. Bonet, B. Instrumentality tests revisited. in Proc. 17th Conf. Uncertainty in Artificial Intelligence 48–55 (Morgan Kaufmann, 2001).

  27. Popescu, S. & Rohrlich, D. Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  28. Carvacho, G. et al. Experimental violation of local causality in a quantum network. Nat. Commun. 8, 14775 (2017).

    Article  ADS  Google Scholar 

  29. Saunders, D. J., Bennet, A. J., Branciard, C. & Pryde, G. J. Experimental demonstration of nonbilocal quantum correlations. Sci. Adv. 3 (2017)

  30. Ringbauer, M. & Chaves, R., Probing the non-classicality of temporal correlations, arXiv preprint arXiv:1704.05469 (2017).

  31. Vazirani, U. & Vidick, T. Fully device-independent quantum key distribution. Phys. Rev. Lett. 113, 140501 (2014).

    Article  ADS  Google Scholar 

  32. Pironio, S. et al. Random numbers certified by Bell’s theorem. Nature 464, 1021–1024 (2010).

    Article  ADS  Google Scholar 

  33. Colbeck, R. & Kent, A. Private randomness expansion with untrusted devices. J. Phys. A 44, 095305 (2011).

  34. Colbeck, R. & Renner, R. Free randomness can be amplified. Nat. Phys. 8, 450–453 (2012).

    Article  Google Scholar 

  35. Gallego, R. et al. Full randomness from arbitrarily deterministic events. Nat. Commun. 4, 2654 (2013).

    Article  Google Scholar 

  36. Brandão, F. G. S. L. et al. Robust device-independent randomness amplification with few devices. Nat. Commun. 7, 11345 (2016).

    Article  ADS  Google Scholar 

  37. Mayers, D. & Yao, A. Self testing quantum apparatus. Quant. Inf. Comput. 4, 273–286 (2004).

    MathSciNet  MATH  Google Scholar 

  38. Chaves, R., Kueng, R., Brask, J. B. & Gross, D. Unifying framework for relaxations of the causal assumptions in Bell’s theorem. Phys. Rev. Lett. 114, 140403 (2015).

    Article  ADS  Google Scholar 

  39. Toner, B. F. & Bacon, D. Communication cost of simulating Bell correlations. Phys. Rev. Lett. 91, 187904 (2003).

    Article  ADS  Google Scholar 

  40. Hall, M. J. W. Local deterministic model of singlet state correlations based on relaxing measurement independence. Phys. Rev. Lett. 105, 250404 (2010).

    Article  ADS  Google Scholar 

  41. Barrett, J. & Gisin, N. How much measurement independence is needed to demonstrate nonlocality? Phys. Rev. Lett. 106, 100406 (2011).

    Article  ADS  Google Scholar 

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R.C. and L.A. acknowledge financial support from the Brazilian ministries MEC and MCTIC. In addition, L.A. is also grateful to the Brazilian agencies CAPES, CNPq, FAPERJ and INCT-IQ for financial support. This work was supported by the ERC-Starting Grant 3D-QUEST (3D-Quantum Integrated Optical Simulation; grant agreement number 307783):, and QUCHIP-Quantum Simulation on a Photonic Chip grant agreement number 641039. G.C. thanks Becas Chile and Conicyt for a doctoral fellowship.

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G.C., I.A, V.D.G, S.G. and F.S. devised and performed the experiment; R.C. and L.A. developed the theoretical tools; all authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Rafael Chaves or Fabio Sciarrino.

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The authors declare no competing financial interests.

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Supplementary Figures 1–6, Supplementary Tables 1–2.

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Chaves, R., Carvacho, G., Agresti, I. et al. Quantum violation of an instrumental test. Nature Phys 14, 291–296 (2018).

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