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A quantum advantage for inferring causal structure


The problem of inferring causal relations from observed correlations is relevant to a wide variety of scientific disciplines. Yet given the correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both. Only a randomized trial can settle the issue. Here we consider the problem of causal inference for quantum variables. We show that the analogue of a randomized trial, causal tomography, yields a complete solution. We also show that, in contrast to the classical case, one can sometimes infer the causal structure from observations alone. We implement a quantum-optical experiment wherein we control the causal relation between two optical modes, and two measurement schemes—with and without randomization—that extract this relation from the observed correlations. Our results show that entanglement and quantum coherence provide an advantage for causal inference.

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Figure 1: The quantum causal inference problem.
Figure 2: Two schemes for probing causal relations and experimental set-up.
Figure 3: Reconstruction of the causal map.
Figure 4: Indicators of causal structure determined by interventionist and observational schemes.

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We thank J. M. Donohue and J. Lavoie for valuable discussions, and M. Mazurek for his assistance in preparing the figures. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Research Chairs, Industry Canada and the Canada Foundation for Innovation (CFI). Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.

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Authors and Affiliations



D.J. and R.W.S. conceived the original idea for the project. K.R. and R.W.S. developed the project and the theory. M.A. and K.J.R. designed the experiment. M.A. and L.V. performed the experiment. M.A., K.R. and K.J.R. performed the numerical calculations. M.A., K.R., K.J.R. and R.W.S. analysed the results. K.R., M.A. and R.W.S. wrote the first draft of the paper and all authors contributed to the final version.

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Correspondence to Katja Ried.

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The authors declare no competing financial interests.

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Ried, K., Agnew, M., Vermeyden, L. et al. A quantum advantage for inferring causal structure. Nature Phys 11, 414–420 (2015).

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