相关论文: Exclusivity principle, Ramsey theory, and $n$-cycl…
The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the…
We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary…
This work explores the implications of the exclusivity principle (EP) in the context of quantum and postquantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary…
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in…
Recently many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are…
Non-contextuality (NC) and Bell inequalities can be expressed as bounds $\Omega$ for positive linear combinations $S$ of probabilities of events, $S \leq \Omega$. Exclusive events in $S$ can be represented as adjacent vertices of a graph…
In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS…
Two ensembles are often used to model random graphs subject to constraints: the microcanonical ensemble (= hard constraint) and the canonical ensemble (= soft constraint). It is said that breaking of ensemble equivalence (BEE) occurs when…
Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognized as a consequence of the exclusivity principle(EP). We provide an operational criterion for monogamy:…
A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates…
We show that the maximum quantum violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality is exactly the maximum value satisfying the following principle: The sum of probabilities of pairwise exclusive events cannot exceed 1. We…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
Ramsey's theorem, in the version of Erd\H{o}s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2,...,n} contains a monochromatic clique of order 1/2\log n. In this paper, we consider two well-studied…
We look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of…
One of the central questions in Ramsey theory asks how small can be the size of the largest clique and independent set in a graph on $N$ vertices. By the celebrated result of Erd\H{o}s from 1947, the random graph on $N$ vertices with edge…
We present a protocol to simulate the quantum correlation implied by non maximally entangled two qubit states, in the worst case scenario. This protocol makes a single use of PR-box and a single use of Millionaire box (M-box). To the best…
Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the…
For a sequence $(H_i)_{i=1}^k$ of graphs, let $\textrm{nim}(n;H_1,\ldots, H_k)$ denote the maximum number of edges not contained in any monochromatic copy of $H_i$ in colour $i$, for any colour $i$, over all $k$-edge-colourings of~$K_n$.…
Given an $r$-uniform hypergraph $H$, the multicolor Ramsey number $r_k(H)$ is the minimum $n$ such that every $k$-coloring of the edges of the complete $r$-uniform hypergraph $K_n^r$ yields a monochromatic copy of $H$. We investigate…
The no-signaling constraints state that the probability distribution of the outputs of any subset of parties is independent of the inputs of the complementary set; here we re-examine these to see how they arise from relativistic causality.…