Universität zu Köln

Glaessle, T., Gross, D. and Chaves, R. (2018). Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling. J. Phys. A-Math. Theor., 51 (48). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121

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Abstract

Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets via quantifier elimination and polyhedral projection algorithms is of primal importance. In this work, before considering specific problems, we review polyhedral projection algorithms with focus on applications in information theory, and, alongside known algorithms, we also present a newly developed geometric algorithm which walks along the face lattice of the polyhedron in the projection space. One important application of this is in the field of quantum non-locality, where marginal problems arise in the computation of Bell inequalities. We apply the discussed algorithms to discover many tight entropic Bell inequalities of the tripartite Bell scenario as well as more complex networks arising in the field of causal inference. Finally, we analyze the usefulness of these inequalities as nonlocality witnesses by searching for violating quantum states.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Glaessle, T. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gross, D. UNSPECIFIED UNSPECIFIED UNSPECIFIED Chaves, R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-164957
DOI:	10.1088/1751-8121/aae754
Journal or Publication Title:	J. Phys. A-Math. Theor.
Volume:	51
Number:	48
Date:	2018
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1751-8121
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUANTIFIER ELIMINATION; SEPARABILITY; ALGORITHM; VERTICES; GEOMETRY Multiple languages Physics, Multidisciplinary; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16495