相关论文: Effectus of Quantum Probability on Relational Stru…

The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a…

Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…

The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…

We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…

The probabilistic interpretation of quantum mechanics has been a point of discussion since the earliest days of the theory. The development of quantum technologies transfer these discussions from philosophical interest to practical…

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…

The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…

Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…

In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…

While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical…

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…

This paper charts a very direct path between the categorical approach to quantum mechanics, due to Abramsky and Coecke, and the older convex-operational approach based on ordered vector spaces (recently reincarnated as "generalized…

A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…

Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how…

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…

The concept of quantum commutativity with respect to an action or coaction of a given Hopf algebra is used for the algebraic description of a system of particles and their interaction with certain quantum field. Graded commutativity and…

We investigate the phenomenon that "every monad is a linear state monad". We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value…