Related papers: Functional boxes, communication complexity and inf…
Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic…
We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only pre-selected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only…
We survey lower-bound results in complexity theory that have been obtained via newfound interconnections between propositional proof complexity, boolean circuit complexity, and query/communication complexity. We advocate for the theory of…
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
There have been a number of attempts to derive the set of quantum non-local correlations from reasonable physical principles. Here we introduce $\tilde{Q}$, a set of multipartite supra-quantum correlations that has appeared under different…
Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of…
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite…
We propose an integration of possibility theory into non-classical logics. We obtain many formal results that generalize the case where possibility and necessity functions are based on classical logic. We show how useful such an approach is…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
We investigate network nonlocality in the triangle scenario when all three parties have no input and binary outputs. Through an explicit example, we prove that this minimal scenario supports nonlocal correlations compatible with…
EXplainable AI has received significant attention in recent years. Machine learning models often operate as black boxes, lacking explainability and transparency while supporting decision-making processes. Local post-hoc explainability…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
Causality is omnipresent in scientists' verbalisations of their understanding, even though we have no formal consensual scientific definition for it. In Automata Networks, it suffices to say that automata "influence" one another to…
What is information, physically, and why does it so reliably emerge in living, cultural, and technological systems? Existing theories quantify uncertainty, cost, or compressibility, but do not identify which physical structures count as…