Related papers: A diagrammatic language for the Causaloid framewor…
Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is…
We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
Humans use causality and hypothetical retrospection in their daily decision-making, planning, and understanding of life events. The human mind, while retrospecting a given situation, think about questions such as "What was the cause of the…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
A powerful strategy to treat quantum field theories beyond perturbation theory is by putting them on a lattice. However, the dynamical and symmetry structure of general relativity have for a long time stood in the way of a well-defined…
Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
We show within the framework of relativistic quantum tasks that the doability of any task is fully determined by a small subset of its parameters that we call its "coarse causal structure", as well as the distributed computation it aims to…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
The aim of this paper is to provide a largely self-contained, compact and comprehensible introduction to the basic ideas behind correlation geometry, which underlies the theory of causal fermion system (CFS). A key focus here is on the…
We develop a bottom-up, statistics-first framework in which the full probabilistic content of an operational theory is encoded in its matrix of conditional outcome probabilities of events (COPE). Within this setting, five model classes…
From the ancient Einstein-Podolsky-Rosen paradox to the recent Sorkin-type impossible measurements problem, the contradictions between relativistic causality, quantum non-locality, and quantum measurement have persisted. Based on quantum…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…