A quantum causal discovery algorithm

Abstract

Finding a causal model for a set of classical variables is now a well-established task---but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally-ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm provides a first step towards more general methods for quantum causal discovery.

11 pages, 10 figures, revised to match published version

References in corpus (8)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
• Inferring causal structure: a quantum advantage
• Quantum Dynamics as an analog of Conditional Probability
• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
• Updating the Born rule
• Quantum Causal Networks

Cited by in corpus (20)

• Bell nonlocality in networks
• Quantum stochastic processes and quantum non-Markovian phenomena
• Non-Markovian Quantum Process Tomography
• Cyclic Quantum Causal Models
• Tensor network based machine learning of non-Markovian quantum processes
• Witnessing quantum memory in non-Markovian processes
• Quantum speedup in the identification of cause-effect relations
• Experimental characterisation of a non-Markovian quantum process
• Quantum Markovianity as a supervised learning task
• Quantum space-time marginal problem: global causal structure from local causal information
• Quantum Causal Models
• Quantum Causal Unravelling
• Anomalous Weak Values Without Post-Selection
• Non-Markovian memory in IBMQX4
• Quantum observation scheme universally identifying causalities from correlations
• Causal influence in operational probabilistic theories
• Multi-time quantum process tomography on a superconducting qubit
• A de Finetti theorem for quantum causal structures
• Quantum causal models via QBism
• Preprocessing operations and the reverse compression