Information–theoretic implications of quantum causal structures

By Rafael Chaves, Christian Majenz, David Gross. 2014

173 citations recorded by the source corpus.

It is a relatively new insight of classical statistics that empirical data can contain information about causation rather than mere correlation. First algorithms have been proposed that are capable of testing whether a presumed causal relationship is compatible with an observed distribution. However, no systematic method is known for treating such problems in a way that generalizes to quantum systems. Here, we describe a general algorithm for computing information–theoretic constraints on the correlations that can arise from a given causal structure, where we allow for quantum systems as well as classical random variables. The general technique is applied to two relevant cases: first, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among some parties. Empirical data can contain information about causation rather than mere correlation. Here Chaves et al. present an algorithm for computing constraints on the correlations arising from a given quantum causal structure, and apply this framework to the information causality principle and networked architectures.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Theory-independent limits on correlations from generalized Bayesian networks (2014, result): “Related work has meanwhile appeared in [9, 30], the latter including extensions of some of our results.”
Quantum common causes and quantum causal models (2016, background): “[11], such as randomness extraction and secure key distribution.”
Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables (2015, methodology): “…of quantum foundations have now begun to apply insights obtained from the study of Bell inequalities to the problem of deriving constraints on observed correlations in more general causal scenarios [14, 19, 20, 21, 22, 23], and the current work constitutes another contribution in this direction.”