A quantum causal discovery algorithm

Christina Giarmatzi,Fabio Costa

doi:10.1038/s41534-018-0062-6

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 opens the route to more general quantum causal discovery methods.

Highlights

The discovery of causal relations is a basic and universal task across all scientific disciplines
The causal relations are represented as arrows in a graph and the causal mechanisms are usually described in terms of transition probabilities (Fig. 1)
This formulation is based on the “combs” formalism for quantum networks,[20] with the main difference that the causal order between events is not assigned in advance

Summary

Introduction

The discovery of causal relations is a basic and universal task across all scientific disciplines. The very nature of causal relations, has been a long-standing subject of controversies with the central question being what, if anything, distinguishes causation from correlation. It is only recently that a rigorous framework for causal discovery has been developed.[1,2] Its core ingredients are causal mechanisms that are responsible for correlations between observed events, with the possibility of external interventions on the events. It is the possibility of interventions that provides an empirically welldefined notion of causation, distinct from correlation: an event A is a cause for an event B if an intervention on A results in a change in the observed statistics of B. The causal relations are represented as arrows in a graph and the causal mechanisms are usually described in terms of transition probabilities (Fig. 1)

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Conclusion