Related papers: Causality in Higher Order Process Theories
We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…
Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…
We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be…
Quantum theory is in principle compatible with scenarios where physical processes occur in an indefinite order, potentially yielding advantages in a broad range of information processing tasks. However, advantages in communication, the most…
Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in Answer-Set Programming, mainly for the purpose of identifying programs that can serve as substitutes without altering…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types communicating processes with mobile channels, a la pi-calculus. Its construction builds on a recent propositions as types correspondence between…
The past decade has seen a remarkable resurgence of the old programme of finding more or less a priori axioms for the mathematical framework of quantum mechanics. The new impetus comes largely from quantum information theory; in contrast to…
Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing…
Tabular synthesis models remain ineffective at capturing complex dependencies, and the quality of synthetic data is still insufficient for comprehensive downstream tasks, such as prediction under distribution shifts, automated…
A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders.…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
We propose a 2-categorical formalism for describing classical information, quantum systems, and their interactions, based on the principle that classical information can be encoded as correlations between quantum systems. Applying this in…
The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In…