Multipartite causal correlations: Polytopes and inequalities

Abbott, AA; Giarmatzi, C; Costa, F; Branciard, C

Multipartite causal correlations: Polytopes and inequalities

Abbott, AA Giarmatzi, C

Costa, F Branciard, C

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Publisher:: AMER PHYSICAL SOC
Publication Type:: Journal Article
Citation:: Physical Review A, 2016, 94, (3)
Issue Date:: 2016-09-30

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Field	Value	Language
dc.contributor.author	Abbott, AA
dc.contributor.author	Giarmatzi, C https://orcid.org/0000-0001-8254-2169
dc.contributor.author	Costa, F
dc.contributor.author	Branciard, C
dc.date.accessioned	2022-08-15T22:18:43Z
dc.date.available	2022-08-15T22:18:43Z
dc.date.issued	2016-09-30
dc.identifier.citation	Physical Review A, 2016, 94, (3)
dc.identifier.issn	2469-9926
dc.identifier.issn	2469-9934
dc.identifier.uri	http://hdl.handle.net/10453/160269
dc.description.abstract	We consider the most general correlations that can be obtained by a group of parties whose causal relations are well defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of parties and inputs and outputs for each party, the set of such correlations forms a convex polytope, whose vertices correspond to deterministic strategies and whose (nontrivial) facets define so-called causal inequalities. We completely characterize the simplest tripartite polytope in terms of its facet inequalities, propose generalizations of some inequalities to scenarios with more parties, and show that our tripartite inequalities can be violated within the process matrix formalism, where quantum mechanics is locally valid but no global causal structure is assumed.
dc.language	English
dc.publisher	AMER PHYSICAL SOC
dc.relation.ispartof	Physical Review A
dc.relation.isbasedon	10.1103/PhysRevA.94.032131
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 02 Physical Sciences, 03 Chemical Sciences
dc.subject.classification	General Physics
dc.title	Multipartite causal correlations: Polytopes and inequalities
dc.type	Journal Article
utslib.citation.volume	94
utslib.for	01 Mathematical Sciences
utslib.for	02 Physical Sciences
utslib.for	03 Chemical Sciences
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access	*
dc.date.updated	2022-08-15T22:18:42Z
pubs.issue	3
pubs.publication-status	Published
pubs.volume	94
utslib.citation.issue	3

Abstract:

We consider the most general correlations that can be obtained by a group of parties whose causal relations are well defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of parties and inputs and outputs for each party, the set of such correlations forms a convex polytope, whose vertices correspond to deterministic strategies and whose (nontrivial) facets define so-called causal inequalities. We completely characterize the simplest tripartite polytope in terms of its facet inequalities, propose generalizations of some inequalities to scenarios with more parties, and show that our tripartite inequalities can be violated within the process matrix formalism, where quantum mechanics is locally valid but no global causal structure is assumed.

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http://hdl.handle.net/10453/160269