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.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Wright, P. G. et al. Tariff on Animal and Vegetable Oils (1928).
Angrist, J. D., Imbens, G. W. & Rubin, D. B. Identification of causal effects using instrumental variables. J. Am. Stat. Assoc. 91, 444–455 (1996).
Greenland, S. An introduction to instrumental variables for epidemiologists. Int. J. Epidemiol. 29, 722–729 (2000).
Balke, A. & Pearl, J. Bounds on treatment effects from studies with imperfect compliance. J. Am. Stat. Assoc. 92, 1171–1176 (1997).
Pearl, J. Causality. (Cambridge Univ. Press, Cambridge, 2009).
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).
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).
Bell, J. S. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964).
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).
Fritz, T. Beyond Bell’s theorem II: Scenarios with arbitrary causal structure. Commun. Math. Phys. 341, 391–434 (2016).
Procopio, L. M. et al. Experimental superposition of orders of quantum gates. Nat. Commun. 6, 7913 (2015).
Rubino, G. et al. Experimental verification of an indefinite causal order. Sci. Adv. 3 (2017), https://doi.org/10.1126/sciadv.1602589.
Henson, J., Lal, R. & Pusey, M. F. Theory-independent limits on correlations from generalized bayesian networks. New J. Phys. 16, 113043 (2014).
Chaves, R., Majenz, C. & Gross, D. Information–theoretic implications of quantum causal structures. Nat. Comm. 6, 5766 (2015).
Pienaar, J. & Brukner, C. A graph-separation theorem for quantum causal models. New J. Phys. 17, 073020 (2015).
Costa, F. & Shrapnel, S. Quantum causal modelling. New J. Phys. 18, 063032 (2016).
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).
Fitzsimons, J., Jones J. & Vedral, V. Quantum correlations which imply causation. arXiv preprint: 1302.2731 (2013).
Ried, K. et al. A quantum advantage for inferring causal structure. Nat. Phys. 11, 414–420 (2015).
MacLean, J.-P. W., Ried, K., Spekkens, R. W. & Resch, K. J. Quantum-coherent mixtures of causal relations. Nat. Comm. 8, 15149 (2017).
Schafer, J. L. & Kang, J. Average causal effects from nonrandomized studies: a practical guide and simulated example. Psychol. Methods 13, 279–313 (2008).
Giacomini, S., Sciarrino, F., Lombardi, E. & De Martini, F. Active teleportation of a quantum bit. Phys. Rev. A 66, 030302 (2002).
Sciarrino, F., Ricci, M., De Martini, F., Filip, R. & Mista, L. Realization of a minimal disturbance quantum measurement. Phys. Rev. Lett. 96, 020408 (2006).
Ringbauer, M. et al. Experimental test of nonlocal causality. Sci. Adv. 2 (2016), https://doi.org/10.1126/sciadv.1600162.
Boyd, S. & Vandenberghe, L. Convex Optimization. (Cambridge Univ. Press, Cambridge, 2004).
Bonet, B. Instrumentality tests revisited. in Proc. 17th Conf. Uncertainty in Artificial Intelligence 48–55 (Morgan Kaufmann, 2001).
Popescu, S. & Rohrlich, D. Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994).
Carvacho, G. et al. Experimental violation of local causality in a quantum network. Nat. Commun. 8, 14775 (2017).
Saunders, D. J., Bennet, A. J., Branciard, C. & Pryde, G. J. Experimental demonstration of nonbilocal quantum correlations. Sci. Adv. 3 (2017) https://doi.org/10.1126/sciadv.1602743.
Ringbauer, M. & Chaves, R., Probing the non-classicality of temporal correlations, arXiv preprint arXiv:1704.05469 (2017).
Vazirani, U. & Vidick, T. Fully device-independent quantum key distribution. Phys. Rev. Lett. 113, 140501 (2014).
Pironio, S. et al. Random numbers certified by Bell’s theorem. Nature 464, 1021–1024 (2010).
Colbeck, R. & Kent, A. Private randomness expansion with untrusted devices. J. Phys. A 44, 095305 (2011).
Colbeck, R. & Renner, R. Free randomness can be amplified. Nat. Phys. 8, 450–453 (2012).
Gallego, R. et al. Full randomness from arbitrarily deterministic events. Nat. Commun. 4, 2654 (2013).
Brandão, F. G. S. L. et al. Robust device-independent randomness amplification with few devices. Nat. Commun. 7, 11345 (2016).
Mayers, D. & Yao, A. Self testing quantum apparatus. Quant. Inf. Comput. 4, 273–286 (2004).
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).
Toner, B. F. & Bacon, D. Communication cost of simulating Bell correlations. Phys. Rev. Lett. 91, 187904 (2003).
Hall, M. J. W. Local deterministic model of singlet state correlations based on relaxing measurement independence. Phys. Rev. Lett. 105, 250404 (2010).
Barrett, J. & Gisin, N. How much measurement independence is needed to demonstrate nonlocality? Phys. Rev. Lett. 106, 100406 (2011).
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): http://www.3dquest.eu, and QUCHIP-Quantum Simulation on a Photonic Chip grant agreement number 641039. G.C. thanks Becas Chile and Conicyt for a doctoral fellowship.
The authors declare no competing financial interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
About this article
Cite this article
Chaves, R., Carvacho, G., Agresti, I. et al. Quantum violation of an instrumental test. Nature Phys 14, 291–296 (2018). https://doi.org/10.1038/s41567-017-0008-5
Physical Review Research (2020)
Physical Review Letters (2020)
Physical Review A (2020)
Physical Review Letters (2020)