Causal Interventions Beyond Time: A CP-do(C)-Calculus for Indefinite Quantum Order

• URL: http://arxiv.org/abs/2508.04737v1
• Date: Tue, 05 Aug 2025 22:49:33 GMT
• Title: Causal Interventions Beyond Time: A CP-do(C)-Calculus for Indefinite Quantum Order
• Authors: Jordi Vallverdu,
• Abstract summary: We reformulate Pearl's three rules of do-calculus in the language of completely positive (CP) trace-preserving maps.<n>We prove that Rule2 fails whenever the underlying process admits indefinite causal order, and we demonstrate this failure in a three-qubit quantum switch'' circuit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We reformulate Pearl's three rules of do-calculus in the language of completely positive (CP) trace-preserving maps, thereby extending them to quantum systems with entanglement. We prove that Rule~2 fails whenever the underlying process admits indefinite causal order, and we demonstrate this failure in a three-qubit ``quantum switch'' circuit. Our analysis clarifies why the classical notions of surgical intervention, faithfulness, and counterfactual dependence must be revised in quantum information science. The CP-do($C$)-calculus introduced here provides a common syntax for causal modelling across classical, definite-order quantum, and indefinite-order quantum regimes.

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