A Semantics for Counterfactuals in Quantum Causal Models

TL;DR

This paper develops a formal framework for evaluating counterfactuals within quantum causal models, extending classical causal semantics to accommodate quantum phenomena and distinguish active from passive counterfactuals.

Contribution

It introduces quantum structural causal models, generalizes Pearl's counterfactual semantics, and demonstrates their increased expressiveness and novel features like counterfactual dependence without causal dependence.

Findings

Quantum counterfactuals can be more expressive than classical ones.

The formalism distinguishes active and passive counterfactuals.

Quantum models can reproduce Bell inequality violations while respecting relativistic causality.

Abstract

We introduce a formalism for the evaluation of counterfactual queries in the framework of quantum causal models, generalising Pearl's semantics for counterfactuals in classical causal models, thus completing the last rung in the quantum analogue of Pearl's "ladder of causation". To this end, we define a suitable extension of Pearl's notion of a 'classical structural causal model', which we denote analogously by 'quantum structural causal model', and a corresponding extension of Pearl's three-step procedure of abduction, action, and prediction. We show that every classical (probabilistic) structural causal model can be extended to a quantum structural causal model, and prove that counterfactual queries that can be formulated within a classical structural causal model agree with their corresponding queries in the quantum extension -- but the latter is more expressive. Counterfactuals in quantum causal models come in different forms: we distinguish between active and passive counterfactual queries, depending on whether or not an intervention is to be performed in the action step. This is in contrast to the classical case, where counterfactuals are always interpreted in the active sense. Another distinctive feature of our formalism is that it breaks the connection between causal and counterfactual dependence that exists in the classical case: quantum counterfactuals allow for counterfactual dependence without causal dependence. This distinction between classical and quantum causal models may shed light on how the latter can reproduce quantum correlations that violate Bell inequalities while being faithful to the relativistic causal structure.