2016/08/31 by Alastair A. Abbott, Christina Giarmatzi, Fabio Costa +1 · 65 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Convex optimization #Convex polytope #Convex set #Formalism (music) #Inequality #Mathematics #Multipartite #Polytope #Probabilistic logic #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Regular polygon #quant-ph
paper · pdf · doi:10.1103/physreva.94.032131
published in Physical Review A 94(3) (American Physical Society) · 14 pages and 1 supplementary CDF file
openalex publication_date 2016/09/30 · arxiv created 2016/10/05 · arxiv updated 2016/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.