Related papers: Graphical Tests of Causality
We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
We consider the most general correlations that can be obtained by a group of parties whose causal relations are well-defined, although possibly probabilistic and dependent on past parties' operations. We show that, for any fixed number of…
Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a…
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 whether every proper (tight) Bell inequality for two parties, other…
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of…
Bell inequality violation is the phenomenon where multiple non-communicating parties can exhibit correlations using quantum resources that are impossible if they can only use classical resources. One way to enforce non-communication is to…
We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding…
The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being…
We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms…
Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, for which several distributed parties attempt to jointly calculate a given…
The Bell numbers count the number of different ways to partition a set of $n$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph…
The existence of a global causal order between events places constraints on the correlations that parties may share. Such "causal correlations" have been the focus of recent attention, driven by the realization that some extensions of…
Bell scenarios are multipartite scenarios that exclude any communication between parties. This constraint leads to a strict hierarchy of correlation sets in such scenarios, namely, classical, quantum, and nonsignaling. However, without any…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
Constraint-based causal discovery algorithms learn part of the causal graph structure by systematically testing conditional independences observed in the data. These algorithms, such as the PC algorithm and its variants, rely on graphical…
In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. This arises naturally when outcomes are difficult to characterize. For instance, if measurements yield smells, it may be…
We study Bell scenarios with binary outcomes supplemented by one bit of classical communication. We develop a method to find facet inequalities for such scenarios even when direct facet enumeration is not possible, or at least difficult.…
We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a…