Abstract
Causality is a seminal concept in science: Any research discipline, from sociology and medicine to physics and chemistry, aims at understanding the causes that could explain the correlations observed among some measured variables. While several methods exist to characterize classical causal models, no general construction is known for the quantum case. In this work, we present quantum inflation, a systematic technique to falsify if a given quantum causal model is compatible with some observed correlations. We demonstrate the power of the technique by reproducing known results and solving open problems for some paradigmatic examples of causal networks. Our results may find applications in many fields: from the characterization of correlations in quantum networks to the study of quantum effects in thermodynamic and biological processes.12 MoreReceived 29 May 2020Revised 1 December 2020Accepted 18 February 2021DOI:https://doi.org/10.1103/PhysRevX.11.021043Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDegree correlationsNonlocalityQuantum foundationsQuantum networksQuantum theoryQuantum Information
Highlights
It can be argued that one of the main challenges in any scientific discipline is to identify which causes are behind the correlations observed among some measured variables, encapsulated by their joint probability distribution
VII, we focus on the study of quantum correlations and use quantum inflation to characterize correlations achievable in various tripartite quantum causal networks, including the derivation of quantum causal incompatibility witnesses
We introduced the quantum inflation technique, a systematic method to discern whether an observable distribution is compatible with a causal explanation involving quantum degrees of freedom
Summary
It can be argued that one of the main challenges in any scientific discipline is to identify which causes are behind the correlations observed among some measured variables, encapsulated by their joint probability distribution. The fundamental task addressed in this work underlies both causal discovery and causal inference and is known as the causal compatibility problem It consists of deciding whether a given joint probability distribution over some observed variables can be (a). The two problems are known to be different, as one of the consequences of Bell’s theorem [4,5] is that quantum causal networks can explain correlations for which the analogous classical network fails [6,7,8,9,10] Our work addresses these issues and provides a systematic construction to tackle the problem of causal compatibility for quantum causal networks. The main result of our work is the construction of quantum inflation, a systematic technique to study causal compatibility in any quantum Bayesian network.
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