Related papers: Categorical Foundations of Quantum Logics and Thei…
This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which…
Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
In the theory of so called "Covariant Quantum Mechanics" a basic role is played by Hermitian vector fields on a complex line bundle in the frameworks of Galilei and Einstein spacetimes. In fact, it has been proved that the Lie algebra of…
We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this…
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples…
Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…
We argue that Anton Zeilinger's "foundational conceptual principle" for quantum mechanics according to which an elementary system carries one bit of information is an idealistic principle, which should be replaced by a realistic principle…
In the topos approach to quantum theory of Doering and Isham the Kochen-Specker Theorem, which asserts the contextual nature of quantum theory, can be reformulated in terms of the global sections of a presheaf characterised by the Gelfand…
We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses.…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…
This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued…
We introduce the notion of a "graded topological space": a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…
This dissertation has two main parts. The first part deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…