2017/08/31 by Alastair A. Abbott, Julian Wechs, Fabio Costa +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Matrix (chemical analysis) #Multipartite #Multipartite entanglement #Order (exchange) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Triangle inequality #quant-ph
paper · pdf · doi:10.22331/q-2017-12-14-39
published as Quantum 1, 39 (2017) · 18 pages, 5 figures, 1 supplementary CDF file
openalex created_date 2017/08/31 · arxiv created 2017/12/13 · openalex publication_date 2017/12/14 · arxiv updated 2017/12/15 · openalex updated_date 2026/08/05
The study of correlations with no definite causal order has revealed a rich structure emerging when more than two parties are involved. This motivates the consideration of multipartite "noncausal" correlations that cannot be realised even if noncausal resources are made available to a smaller number of parties. Here we formalise this notion: genuinely N-partite noncausal correlations are those that cannot be produced by grouping N parties into two or more subsets, where a causal order between the subsets exists. We prove that such correlations can be characterised as lying outside a polytope, whose vertices correspond to deterministic strategies and whose facets define what we call "2-causal" inequalities. We show that genuinely multipartite noncausal correlations arise within the process matrix formalism, where quantum mechanics holds locally but no global causal structure is assumed, although for some inequalities no violation was found. We further introduce two refined definitions that allow one to quantify, in different ways, to what extent noncausal correlations correspond to a genuinely multipartite resource.