Inflation: A Python Library For Classical And Quantum Causal Compatibility

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Emanuel-Cristian Boghiu¹, Elie Wolfe², and Alejandro Pozas-Kerstjens³

¹ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, Canada, N2L 2Y5
³Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain

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Abstract

We introduce Inflation, a Python library for assessing whether an observed probability distribution is compatible with a causal explanation. This is a central problem in both theoretical and applied sciences, which has recently witnessed significant advances from the area of quantum nonlocality, namely, in the development of inflation techniques. Inflation is an extensible toolkit that is capable of solving pure causal compatibility problems and optimization over (relaxations of) sets of compatible correlations in both the classical and quantum paradigms. The library is designed to be modular and with the ability of being ready-to-use, while keeping an easy access to low-level objects for custom modifications.

Featured image: Left: The triangle scenario, whereby the values of three visible random variables, $A$, $B$, and $C$, are influenced each by two different out of the three latent variables $rho_{AB}$, $rho_{BC}$ and $rho_{AC}$. These latent variables can be chosen to be either sources of shared randomness or of quantum states. Each party creates the value of their random variable by operating on the systems received, as in $E_a$. Answering whether a probability distribution over the values output by $A$, $B$ and $C$ is compatible with this structure is a numerically hard problem.

Right: The second-order quantum inflation of the triangle scenario. Inflation considers copies of the states and measurements as depicted. The use of copies of the original elements implies many symmetries, so distributions compatible with this scenario can be characterized via semidefinite programming.

Popular summary

One of the main challenges in science is identifying which are the causes behind some observed correlations. Is a vaccine effective against a disease? Does raising salaries encourage spending? All these questions can be formulated analyzed using the tools of causal inference, but are often numerically hard to answer. Recently, new tools have appeared in the field of quantum nonlocality, called inflation methods, that allow to relax these hard problems to numerically tractable ones. In this work we present a Python package that implements such methods.

► BibTeX data

@article{Boghiu2023inflationpython, doi = {10.22331/q-2023-05-04-996}, url = {https://doi.org/10.22331/q-2023-05-04-996}, title = {Inflation: a {P}ython library for classical and quantum causal compatibility}, author = {Boghiu, Emanuel-Cristian and Wolfe, Elie and Pozas-Kerstjens, Alejandro}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {996}, month = may, year = {2023}
}

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[1] Robin Lorenz and Sean Tull, "Causal models in string diagrams", arXiv:2304.07638, (2023).

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2023-05-04-996/

Time Stamp: May 4, 2023

Time Stamp: Oct 13, 2022

Republished By Plato

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