2014/09/30 by Salman Beigi, Amin Gohari
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Discrete mathematics #Generalization #Geometry #Locality #Mathematical analysis #Mathematics #Monotone polygon #Monotonic function #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Set (abstract data type) #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1109/tit.2015.2452253
published as IEEE Transactions on Information Theory 61(9), 5185-5208 (2015) · 39 pages, 1 table, 3 figures, final version
openalex publication_date 2015/07/07 · arxiv created 2017/01/11 · arxiv updated 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Non-locality is the phenomenon of observing strong correlations among the outcomes of local measurements of a multipartite physical system. No-signaling boxes are the abstract objects for studying non-locality, and wirings are local operations on the space of no-signaling boxes. This means that, no matter how non-local the nature is, the set of physical non-local correlations must be closed under wirings. Then, one approach to identify the non-locality of nature is to characterize the closed sets of non-local correlations. Although non-trivial examples of wirings of no-signaling boxes are known, there is no systematic way to study wirings. In particular, given a set of no-signaling boxes, we do not know a general method to prove that it is closed under wirings. In this paper, we propose the first general method to construct such closed sets of non-local correlations. We show that a well-known measure of correlation, called maximal correlation, when appropriately defined for non-local correlations, is monotonically decreasing under wirings. This establishes a conjecture about the impossibility of simulating isotropic boxes from each other, implying the existence of a continuum of closed sets of non-local boxes under wirings. To prove our main result, we introduce some mathematical tools that may be of independent interest: we define a notion of maximal correlation ribbon as a generalization of maximal correlation, and provide a connection between it and a known object called hypercontractivity ribbon; we show that these two ribbons are monotone under wirings too.