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L6-03 · Quantum DAGs and Markov assumptions

State a quantum causal model before using its graph.

Level 6 icon Level 6 · Graduate
Objective. State a quantum causal model before using its graph.
Before this lesson. L6-01, L6-02, L4-02
Hands-on lab. Confounding and intervention

Learn

A directed acyclic graph records candidate causal connections without directed cycles. In a quantum model, arrows can carry quantum systems. A node can represent a laboratory with input and output spaces. The graph alone does not specify its channel or measurement probabilities.

A quantum Markov condition connects the graph with a restricted operator structure. The exact condition depends on the formalism. Independent mechanisms and local operational choices must be defined. Do not replace all scalar probabilities in a classical factorization by arbitrary matrices and multiply them blindly.

An absent arrow states a restriction on possible influence within the model. An observed zero correlation does not prove an absent arrow. A mechanism can cancel or hide an influence for particular preparations. Model checks therefore require suitable interventions or a stated faithfulness assumption.

Practice

Solution

A hidden environment that retains memory across the two stages can break the description. An unmodelled common cause of the laboratories can also require a larger joint process.

Check your understanding

Does one zero correlation prove that a causal edge is absent?

Show the answer

B. No, a mechanism can hide the influence

A present mechanism can give zero dependence for a particular state or setting. Structural conclusions require additional assumptions or informative interventions.

Sources

This lesson draws on Allen et al., 2017Costa & Shrapnel, 2016.

Next: L6-04 · Operational interventions

References
  1. Allen, J.-M. A., Barrett, J., Horsman, D. C., Lee, C. M., & Spekkens, R. W. (2017). Quantum common causes and quantum causal models. Physical Review X, 7(3). 10.1103/PhysRevX.7.031021
  2. Costa, F., & Shrapnel, S. (2016). Quantum causal modelling. New Journal of Physics, 18(6), 063032. 10.1088/1367-2630/18/6/063032