Causal Interventions Beyond Time: A CP-do(C)-Calculus for Indefinite Quantum Order
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908480761233408 |
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| author | Vallverdu, Jordi |
| author_facet | Vallverdu, Jordi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Causal Interventions Beyond Time: A CP-do(C)-Calculus for Indefinite Quantum Order Vallverdu, Jordi Quantum Physics 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. |
| title | Causal Interventions Beyond Time: A CP-do(C)-Calculus for Indefinite Quantum Order |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.04737 |