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Quantum Causal Models
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Quantum Causal Models
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It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this work leaves open whether causal concepts are fundamental to quantum theory, or only find application at an emergent level of classical devices and measurement outcomes. Here, we present a framework of quantum causal models, with causal relations defined in terms intrinsic to quantum theory, and the central object of study being the quantum process itself. Following Allen et al., Phys. Rev. X 7, 031021 (2017), the approach defines quantum causal relations in terms of unitary evolution, in a way analogous to an approach to classical causal models that assumes underlying determinism and situates causal relations in functional dependences between variables. We show that any unitary quantum circuit has a causal structure corresponding to a directed acyclic graph, and that when marginalising over local noise sources, the resulting quantum process satisfies a Markov condition with respect to the graph. We also prove a converse to this statement. We introduce an intrinsically quantum notion that plays a role analogous to the conditional independence of classical variables, and (generalizing a central theorem of the classical framework) show that d-separation is sound and complete for it in the quantum case. We present generalizations of the three rules of the classical do-calculus, in each case relating a property of the causal structure to a formal property of the quantum process, and to an operational statement concerning the outcomes of interventions. In addition, we introduce and derive similar results for classical split-node causal models, which are more closely analogous to quantum causal models than the classical causal models that are usually studied.
Forward citations
Cited by 7 Pith papers
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Impossibility of superluminal signalling rules out causal loops in conical spacetimes
In conical spacetimes with d>1, NSS prohibits operationally detectable causal loops across classical, quantum and post-quantum theories, unlike the (1+1) case.
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Higher-Order Programs with Indefinite Causal Orders: a Linear Approach to Coherent Control of Quantum Processes
A linear-typed higher-order language realises indefinite causal orders on general quantum channels (including measurements), with soundness in Caus[CPM] and expressivity covering all first-order channels plus a large ...
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Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities
Quasiprobability models in Bayesian networks generalize to produce all non-signalling correlations for a broad class of networks and conjecturally recover the nested Markov model.
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Characterizing Signalling: Connections between Causal Inference and Space-time Geometry
Introduces the order-theoretic property of conicality for space-times and proves a correspondence between conical space-times and faithful information-theoretic causal models under no-superluminal-signalling constraints.
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Theories with no superluminal signaling have greater information-processing power than theories with no superluminal causation
Theories obeying no superluminal signaling but violating no superluminal causation can achieve non-classical tasks impossible under no superluminal causation, including certifiable retrocausality in Minkowski spacetime.
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On the Conicality of Causally Simple, Future Cohesive Spacetimes
Causally simple future cohesive spacetimes satisfy conicality in dimension at least 3, unlike those that are merely homotopy equivalent to Minkowski or globally hyperbolic.
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Decoherence without the state: A causal quantum Darwinist approach
Decoherence is recast as causal information proliferation in unitary circuits, with dual decoherence selecting privileged consistent histories and letting states and outcomes emerge.
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