Abstract
Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces ‘spooky’ hidden mechanisms. Whether one can produce a genuinely quantum framework in order to discover causal structure remains an open question. Here we introduce a new framework for quantum causal modelling that allows for the discovery of causal structure. We define quantum analogues for core features of classical causal modelling techniques, including the causal Markov condition and faithfulness. Based on the process matrix formalism, this framework naturally extends to generalised structures with indefinite causal order.
Highlights
Why causeCausality often appears as an axiom in the formulation of physical theories, typically as the assumption that effects cannot precede their causes
This work has foundational implications insofar as it shows that quantum mechanics has a causal interpretation in a similar manner to classical mechanics
Causeeffect relations are identified with correlations between controlled and observed events, and a causal structure is a set of transformations that define a directed acyclic graph (DAG)
Summary
Causality often appears as an axiom in the formulation of physical theories, typically as the assumption that effects cannot precede their causes. The recent technical developments of causal modelling provide a consistent mathematical formalism that relates causal influence to the possibility of signalling [1, 2]. Causal models have proved tremendously useful for understanding causal relations across a broad range of disciplines They provide a powerful mathematical toolbox for efficiently extracting causal information from observed data, Figs. Causal models presume the existence of objective properties that can be observed and manipulated locally Such assumptions are incompatible with quantum mechanics, as most promin-. [21], a key missing step is the formulation of a quantum version of the causal Markov condition In classical models, this condition enables one to use observational and interventionist inference to deduce causal structure from data. A formalism for quantum causal modelling would require a similar condition
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