International Journal of Advance Research Publication and Reviews

International Journal of Advance Research Publication and Reviews
Peer-Reviewed | Multi-Disciplinary Journal

ISSN: 3049-0103 (O)

Impact Factor: 4.33

Informational Pruning as a Third Path: Final-State Constraints between Consistent Quantum Causes and Quantum Causal Models

Author

Ian Staley

Abstract

 Two recent programs offer competing accounts of quantum causation. Griffiths' Consistent Quantum Causes grounds causal reasoning in the Consistent Histories formalism, treating stochastic time development and noncommuting projectors as the foundation for a Pearl-style causal graph. The Costa and Shrapnel Quantum Causal Models program takes the process-matrix formalism as its starting point and extends naturally to indefinite causal order. Both assume causal structure is fixed by an initial condition and forward dynamics, and neither addresses admissibility conditioned at both temporal boundaries. This paper argues that final-state-constrained history ensembles, and the informational pruning they induce, provide a third vantage point on the two programs. The claim is not that the disagreement is resolved, but that once admissibility is globally filtered by an initial and a final boundary condition, the question of which coarse-grained histories carry the effective causal structure of the process is reframed. The Hartle and Craig rank-product theorem supplies the formal backbone, and the three-box paradox provides a worked illustration in which the filter reduces two framework choices to one admissible history each and excludes the third. An explainability stance, drawn methodologically from explainable artificial intelligence, sharpens which admissible histories do the explanatory work.


Keywords

Consistent histories; quantum causal models; final boundary condition; informational pruning; rank-product theorem; three-box paradox

Full Text:

Download Paper PDF

References

  • Adlam, E. (2023). Is there causation in fundamental physics? New insights from process matrices and quantum causal modelling. Synthese, 201(5), Article 152. https://doi.org/10.1007/s11229-023-04160-z
  • Adlam, E., Hance, J. R., Hossenfelder, S., & Palmer, T. N. (2024). Taxonomy for physics beyond quantum mechanics. Proceedings of the Royal Society A, 480(2294), Article 20230779. https://doi.org/10.1098/rspa.2023.0779
  • Aharonov, Y., Bergmann, P. G., & Lebowitz, J. L. (1964). Time symmetry in the quantum process of measurement. Physical Review, 134(6B), B1410-B1416. https://doi.org/10.1103/PhysRev.134.B1410
  • Aharonov, Y., & Vaidman, L. (1990). Properties of a quantum system during the time interval between two measurements. Physical Review A, 41(1), 11-20. https://doi.org/10.1103/PhysRevA.41.11
  • Aharonov, Y., & Vaidman, L. (1991). Complete description of a quantum system at a given time. Journal of Physics A: Mathematical and General, 24(10), 2315-2328. https://doi.org/10.1088/0305-4470/24/10/018
  • Anastopoulos, C. (2025). Final states in quantum cosmology: Cosmic acceleration as a quantum postselection effect. Physical Review D, 111(6), Article 064045. https://doi.org/10.1103/PhysRevD.111.064045
  • Barrett, J., Friend, I., & Kissinger, A. (2025). Quantum and classical Markovian graphical causal models and their identification. In J. Endrullis & S. Schmitz (Eds.), 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)(Leibniz International Proceedings in Informatics Vol. 326, pp. 48:1-48:23). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.CSL.2025.48
  • Chiribella, G., D'Ariano, G. M., Perinotti, P., & Valiron, B. (2013). Quantum computations without definite causal structure. Physical Review A, 88(2), Article 022318. https://doi.org/10.1103/PhysRevA.88.022318
  • Costa, F., Barrett, J., & Shrapnel, S. (2025). A de Finetti theorem for quantum causal structures. Quantum, 9, Article 1628. https://doi.org/10.22331/q-2025-02-11-1628
  • Costa, F., & Shrapnel, S. (2016). Quantum causal modelling. New Journal of Physics, 18(6), Article 063032. https://doi.org/10.1088/1367-2630/18/6/063032
  • Craig, D. A. (1997). The geometry of consistency: Decohering histories in generalized quantum theory[Preprint]. arXiv. https://arxiv.org/abs/quant-ph/9704031
  • Dowker, F., & Kent, A. (1996). On the consistent histories approach to quantum mechanics. Journal of Statistical Physics, 82(5-6), 1575-1646. https://doi.org/10.1007/BF02183396
  • Evans, P. W. (2018). Quantum causal models, faithfulness, and retrocausality. The British Journal for the Philosophy of Science, 69(3), 745-774. https://doi.org/10.1093/bjps/axw037
  • Gell-Mann, M., & Hartle, J. B. (1993). Classical equations for quantum systems. Physical Review D, 47(8), 3345-3382. https://doi.org/10.1103/PhysRevD.47.3345
  • Gell-Mann, M., & Lloyd, S. (2004). Effective complexity. In M. Gell-Mann & C. Tsallis (Eds.), Nonextensive entropy: Interdisciplinary applications(pp. 387-398). Oxford University Press.
  • Giarmatzi, C., & Costa, F. (2018). A quantum causal discovery algorithm. npj Quantum Information, 4, Article 17. https://doi.org/10.1038/s41534-018-0062-6
  • Griffiths, R. B. (1984). Consistent histories and the interpretation of quantum mechanics. Journal of Statistical Physics, 36(1-2), 219-272. https://doi.org/10.1007/BF01015734
  • Griffiths, R. B. (2002). Consistent quantum theory. Cambridge University Press.
  • Griffiths, R. B. (2024). Consistent quantum causes[Preprint]. arXiv. https://arxiv.org/abs/2303.13617
  • Hartle, J. B. (2020). Arrows of time and initial and final conditions in the quantum mechanics of closed systems like the universe[Preprint]. arXiv. https://arxiv.org/abs/2002.07093
  • Heese, R., Gerlach, T., Mücke, S., Müller, S., Jakobs, M., & Piatkowski, N. (2025). Explaining quantum circuits with Shapley values: Towards explainable quantum machine learning. Quantum Machine Intelligence, 7(1), Article 27. https://doi.org/10.1007/s42484-025-00254-8
  • Kastner, R. E. (1999). The three-box “paradox” and other reasons to reject the counterfactual usage of the ABL rule. Foundations of Physics, 29(6), 851-863. https://doi.org/10.1023/A:1018865010735
  • Leifer, M. S., & Pusey, M. F. (2017). Is a time symmetric interpretation of quantum theory possible without retrocausality? Proceedings of the Royal Society A, 473(2202), Article 20160607. https://doi.org/10.1098/rspa.2016.0607
  • Molnar, C. (2022). Interpretable machine learning: A guide for making black box models explainable(2nd ed.). Leanpub.
  • Oreshkov, O., Costa, F., & Brukner, Č. (2012). Quantum correlations with no causal order. Nature Communications, 3, Article 1092. https://doi.org/10.1038/ncomms2076
  • Ormrod, N., & Barrett, J. (2024). Quantum influences and event relativity[Preprint]. arXiv. https://arxiv.org/abs/2401.18005
  • Pira, L., & Ferrie, C. (2024). On the interpretability of quantum neural networks. Quantum Machine Intelligence, 6(2), Article 52. https://doi.org/10.1007/s42484-024-00191-y
  • Price, H., & Wharton, K. (2017). Dispelling the quantum spooks: A clue that Einstein missed? In C. Bouton & P. Huneman (Eds.), Time of nature and the nature of time(Boston Studies in the Philosophy and History of Science Vol. 326, pp. 123-137). Springer. https://doi.org/10.1007/978-3-319-53725-2_7
  • Ribeiro, M. T., Singh, S., & Guestrin, C. (2016). “Why should I trust you?”: Explaining the predictions of any classifier. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining(pp. 1135-1144). Association for Computing Machinery. https://doi.org/10.1145/2939672.2939778
  • Ried, K., Agnew, M., Vermeyden, L., Janzing, D., Spekkens, R. W., & Resch, K. J. (2015). A quantum advantage for inferring causal structure. Nature Physics, 11(5), 414-420. https://doi.org/10.1038/nphys3266
  • Rozema, L. A., Strömberg, T., Cao, H., Guo, Y., Liu, B.-H., & Walther, P. (2024). Experimental aspects of indefinite causal order in quantum mechanics. Nature Reviews Physics, 6(8), 483-499. https://doi.org/10.1038/s42254-024-00739-8
  • Shrapnel, S. (2019). Discovering quantum causal models. The British Journal for the Philosophy of Science, 70(1), 1-25. https://doi.org/10.1093/bjps/axx044
  • Staley, I. (2026). Final-state constraints and informational pruning in quantum histories. International Journal of Quantum Foundations, 12(2), 719-737. https://doi.org/10.5281/zenodo.19512844
  • Strasberg, P., Reinhard, T. E., & Schindler, J. (2024). First principles numerical demonstration of emergent decoherent histories. Physical Review X, 14(4), Article 041027. https://doi.org/10.1103/PhysRevX.14.041027
Top