On the Significance of Intermediate Latents: Distinguishing Quantum Causal Scenarios with Indistinguishable Classical Analogs

TL;DR

This paper explores how quantum interpretations of latent variables in causal models can distinguish scenarios that are indistinguishable under classical assumptions, especially focusing on intermediate latent nodes and their operational implications.

Contribution

It introduces a framework for differentiating quantum causal structures with intermediate latent nodes using monogamy of nonlocality and semidefinite relaxations, highlighting new quantum-classical distinctions.

Findings

Quantum latent nodes can be distinguished via nonlocality monogamy.

Semidefinite relaxations help operationally differentiate quantum causal scenarios.

Many quantum processes with intermediate latents are distinguishable from classical models.

Abstract

The use of graphical models to represent causal hypotheses has enabled revolutionary progress in the study of the foundations of quantum theory. Here we consider directed acyclic graphs each of which contains both nodes representing observed variables as well as nodes representing latent or hidden variables. When comparing distinct causal structure, a natural question to ask is if they can explain distinct sets of observable distributions or not. Statisticians have developed a great variety of tools for resolving such questions under the assumption that latent nodes be interpreted classically. Here we highlight how the change to a quantum interpretation of the latent nodes induces distinctions between causal scenarios that would be classically indistinguishable. We especially concentrate on quantum scenarios containing latent nodes with at least one latent parent, a.k.a. possessing intermediate latents. This initial survey demonstrates that many such quantum processes can be operationally distinguished by considerations related to monogamy of nonlocality, especially when computationally aided by a hierarchy of semidefinite relaxations which we tailor for the study such scenarios. We conclude by clarifying the challenges that prevent the generalization of this work, calling attention to open problems regarding observational (in)equivalence of quantum causal structures with intermediate latents.