Quantum and Classical Markovian Graphical Causal Models and Their Identification

Authors Jonathan Barrett , Isaac Friend , Aleks Kissinger



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Author Details

Jonathan Barrett
  • University of Oxford, UK
Isaac Friend
  • University of Oxford, UK
Aleks Kissinger
  • University of Oxford, UK

Acknowledgements

We thank Elie Wolfe and Rob Spekkens for insights regarding the classes of instruments that can be used for causal identification.

Cite As Get BibTex

Jonathan Barrett, Isaac Friend, and Aleks Kissinger. Quantum and Classical Markovian Graphical Causal Models and Their Identification. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 48:1-48:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CSL.2025.48

Abstract

Markov categories allow formalization of probabilistic and causal reasoning in a general setting that applies uniformly to many different kinds of classical probabilistic processes. It has so far been challenging, however, to generalize these techniques to reasoning about quantum processes, as the quantum no-cloning theorem forbids "copy" maps of the sort that have been used to axiomatize conditional independence, and the related notions of complete common causes and Markovianity, in classical Bayesian networks. Here, we introduce a new categorical notion of Markovian causal model, according to which a distinguished subcategory of "common cause" maps plays a similar role to that of "copy" maps in the categorical formulation of Bayesian networks. Moreover, defining causal models as second-order processes yields a clean and flexible formulation of interventions. Our formalism is both rich enough to handle "complete common cause" assumptions and general enough to encompass not only standard classical causal identification scenarios, but also quantum causal scenarios and new kinds of classical causal identification based on imperfect observations. Furthermore, we show that one can reason uniformly across all of these cases using string-diagrammatic techniques.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Causal reasoning and diagnostics
  • Theory of computation → Categorical semantics
  • Theory of computation → Quantum computation theory
Keywords
  • causal inference
  • Bayesian networks
  • quantum combs
  • process theories

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References

  1. John-Mark A. Allen, Jonathan Barrett, Dominic C. Horsman, Ciarán M. Lee, and Robert W. Spekkens. Quantum Common Causes and Quantum Causal Models. Phys. Rev. X, 7(3):031021, July 2017. URL: https://doi.org/10.1103/PhysRevX.7.031021.
  2. Howard Barnum, Carlton M. Caves, Christopher A. Fuchs, Richard Jozsa, and Benjamin Schumacher. Noncommuting Mixed States Cannot Be Broadcast. Phys. Rev. Lett., 76(15):2818-2821, April 1996. Publisher: American Physical Society. URL: https://doi.org/10.1103/PhysRevLett.76.2818.
  3. Jonathan Barrett, Robin Lorenz, and Ognyan Oreshkov. Quantum Causal Models, 2019. URL: https://doi.org/10.48550/arXiv.1906.10726.
  4. G. Chiribella, G. M. D'Ariano, and P. Perinotti. Quantum Circuit Architecture. Phys. Rev. Lett., 101(6):060401, August 2008. Publisher: American Physical Society. URL: https://doi.org/10.1103/PhysRevLett.101.060401.
  5. Bob Coecke and Aleks Kissinger. Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, 2017. URL: https://doi.org/10.1017/9781316219317.
  6. Bob Coecke and Robert W. Spekkens. Picturing classical and quantum Bayesian inference. Synthese, 186(3):651-696, June 2012. URL: https://doi.org/10.1007/s11229-011-9917-5.
  7. Juan D. Correa, Jin Tian, and Elias Bareinboim. Identification of Causal Effects in the Presence of Selection Bias. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01):2744-2751, July 2019. Section: AAAI Technical Track: Knowledge Representation and Reasoning. URL: https://doi.org/10.1609/aaai.v33i01.33012744.
  8. Fabio Costa and Sally Shrapnel. Quantum causal modelling. New Journal of Physics, 18(6):063032, June 2016. Publisher: IOP Publishing. URL: https://doi.org/10.1088/1367-2630/18/6/063032.
  9. Isaac Friend and Aleks Kissinger. Identification of Causal Influences in Quantum Processes. In Stefano Gogioso and Matty Hoban, editors, Proceedings 19th International Conference on Quantum Physics and Logic, Wolfson College, Oxford, UK, 27 June - 1 July 2022, volume 394 of Electronic Proceedings in Theoretical Computer Science, pages 101-115. Open Publishing Association, 2023. URL: https://doi.org/10.4204/EPTCS.394.7.
  10. Isaac Friend and Aleks Kissinger. Identification of causal influences in quantum processes. Physical Review A, 109(4):042214, April 2024. Publisher: American Physical Society. URL: https://doi.org/10.1103/PhysRevA.109.042214.
  11. Tobias Fritz. A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics. Advances in Mathematics, 370:107239, August 2020. URL: https://doi.org/10.1016/j.aim.2020.107239.
  12. Christina Giarmatzi and Fabio Costa. A quantum causal discovery algorithm. npj Quantum Information, 4(1):17, March 2018. URL: https://doi.org/10.1038/s41534-018-0062-6.
  13. Bart Jacobs, Aleks Kissinger, and Fabio Zanasi. Causal Inference by String Diagram Surgery. In Mikołaj Bojańczyk and Alex Simpson, editors, Foundations of Software Science and Computation Structures, pages 313-329, Cham, 2019. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-17127-8_18.
  14. Bart Jacobs and Fabio Zanasi. The Logical Essentials of Bayesian Reasoning. CoRR, abs/1804.01193, 2018. arXiv: 1804.01193. URL: https://arxiv.org/abs/1804.01193.
  15. M. S. Leifer and Robert W. Spekkens. Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference. Phys. Rev. A, 88(5):052130, November 2013. Publisher: American Physical Society. URL: https://doi.org/10.1103/PhysRevA.88.052130.
  16. Judea Pearl. Causality. Cambridge University Press, 2 edition, 2009. URL: https://doi.org/10.1017/CBO9780511803161.
  17. Katja Ried, Megan Agnew, Lydia Vermeyden, Dominik Janzing, Robert W. Spekkens, and Kevin J. Resch. A quantum advantage for inferring causal structure. Nature Physics, 11(5):414-420, May 2015. URL: https://doi.org/10.1038/nphys3266.
  18. Benjamin Schumacher and Michael D. Westmoreland. Locality and Information Transfer in Quantum Operations. Quantum Information Processing, 4(1):13-34, February 2005. URL: https://doi.org/10.1007/s11128-004-3193-y.
  19. Sally Shrapnel, Fabio Costa, and Gerard Milburn. Quantum Markovianity as a supervised learning task. International Journal of Quantum Information, 16(08):1840010, 2018. URL: https://doi.org/10.1142/S0219749918400105.
  20. W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299(5886):802-803, October 1982. URL: https://doi.org/10.1038/299802a0.
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