Gláucia Murta

Characterizing the performance of XOR games and the Shannon capacity of graphs.

In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party XOR game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games that have no quantum advantage for arbitrary input probability distributions, up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum nonlocal correlations.

Tightness of correlation inequalities with no quantum violation

We study the faces of the set of quantum correlations, i.e., the Bell and noncontextuality inequalities without any quantum violation. First, we investigate the question of whether every proper (facet-defining) Bell inequality for two parties, other than the trivial ones from positivity, normalization, and no-signaling, can be violated by quantum correlations, i.e., whether the classical Bell polytope or the smaller correlation polytope share any facets with their respective quantum sets. To do this, we develop a recently derived bound on the quantum value of linear games based on the norms of game matrices to give a simple sufficient condition to identify linear games with no quantum advantage. Additionally we show how this bound can be extended to the general class of unique games. We then show that the paradigmatic examples of correlation Bell inequalities with no quantum violation, namely the nonlocal computation games, do not constitute facet-defining Bell inequalities, not even for the correlation polytope. We also extend this to an arbitrary prime number of outcomes for a specific class of these games. We then study the faces in the simplest Clauser-Horne-Shimony-Holt Bell scenario of binary dichotomic measurements, and identify edges in the set of quantum correlations in this scenario. Finally, we relate the noncontextual polytope of single-party correlation inequalities with the cut polytope

Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement

\text{CUT}(\mathbf{\ensuremath{\nabla}}G)

Bounds on quantum nonlocality via partial transposition

, where

Genuine-multipartite entanglement criteria based on positive maps

G

Generalized XOR games with d outcomes and the task of nonlocal computation

denotes the compatibility graph of observables in the contextuality scenario and

XOR games with

\mathbf{\ensuremath{\nabla}}G

d

denotes the suspension graph of

outcomes and the task of non-local computation

G

Generalized xor games withdoutcomes and the task of nonlocal computation

. We observe that there exist facet-defining noncontextuality inequalities with no quantum violation, and furthermore that this set of inequalities is beyond those implied by the consistent exclusivity principle.