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.


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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): 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.

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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). https://doi.org/10.1038/s41567-017-0008-5

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