Related papers: Graph-Theoretic Approach to Quantum Correlations
We investigate vector chromatic number, Lovasz theta of the complement, and quantum chromatic number from the perspective of graph homomorphisms. We prove an analog of Sabidussi's theorem for each of these parameters, i.e. that for each of…
This paper delves into three research directions, leveraging the Lov\'{a}sz $\vartheta$-function of a graph. First, it focuses on the Shannon capacity of graphs, providing new results that determine the capacity for two infinite subclasses…
The boundary between classical and quantum correlations is well characterised by linear constraints called Bell inequalities. It is much harder to characterise the boundary of the quantum set itself in the space of no-signaling…
It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations,…
The Hoffman ratio bound, Lov\'{a}sz theta function and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics and information theory. By using…
This paper addresses the behavior of the Lov\'asz number for dense random circulant graphs. The Lov\'asz number is a well-known semidefinite programming upper bound on the independence number. Circulant graphs, an example of a Cayley graph,…
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and…
We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the…
Sequential measurements on a single particle play an important role in fundamental tests of quantum mechanics. We provide a general method to analyze temporal quantum correlations, which allows us to compute the maximal correlations for…
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs…
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations of the two-particle Laplacian including such interactions…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of…
The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly…
What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties…
We show, for any finite $n \geq 2$, that there exist quantum correlations obtained from performing $n$ dichotomic quantum measurements in a bipartite Bell scenario, which cannot be reproduced by mixtures of measurement devices with at most…
Simulation tasks are insightful tools to compare information-theoretic resources. Considering a generalization of usual Bell scenarios where external quantum inputs are provided to the parties, we show that any entangled quantum state…