Related papers: Graph-Theoretic Approach to Quantum Correlations
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…
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure of a set of events (a graph), and its…
Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely, with minimal assumptions about the underlying quantum system. It is based on the observation that some extremal points in the…
The CHSH inequalities are the most famous examples of Bell inequalities. Cabello, Severini, and Winter (CSW) came up with a graph approach to noncontextuality inequalities, which connects some graph-theoretic concepts to quantum and…
We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lov\'asz number which is equal to its fractional packing number. The…
Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly,…
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality…
Quantum correlations arising in Bell experiments, involving a physical source that emits a quantum state to a number of observers, have been intensively studied over the last decades. Much less is known about the nature of quantum…
A homomorphism from a graph $X$ to a graph $Y$ is an adjacency preserving mapping $f:V(X) \rightarrow V(Y)$. We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph $X$ admits a…
Quantum contextuality is usually revealed by the non-contextual inequality, which can always be associated with an exclusivity graph. The quantum upper bound of the inequality is nothing but the Lov\'asz number of the graph. In this work,…
Measurement incompatibility--the impossibility of jointly measuring certain quantum observables--is a fundamental resource for quantum information processing. We develop a graph-theoretic framework for quantifying this resource for large…
It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…
We introduce a novel technique to give bounds to the entangled value of non-local games. The technique is based on a class of graphs used by Cabello, Severini and Winter in 2010. The upper bound uses the famous Lov\'asz theta number and is…
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in Quantum theory is an intriguing one in this…
Lov\'asz's bound to the capacity of a graph and the the sphere-packing bound to the probability of error in channel coding are given a unified presentation as information radii of the Csisz\'ar type using the R{\'e}nyi divergence in the…
We demonstrate that quantum correlations can emerge from the statistical correlations of random discrete models, without an a priori assumption that the random models are quantum mechanical in nature, that is without considering…
We address the problem of deriving the set of quantum correlations for every Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We show that the correlations that are possible according to quantum theory are equal…
Quantum theory predicts and experiments confirm that nature can produce correlations between distant events that are nonlocal in the sense of violating a Bell inequality. Nevertheless, Bell's strong sentence {\it Correlations cry out for…
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…
Bell nonlocality -- the existence of quantum correlations that cannot be explained by classical means -- is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is…