Related papers: Sheaf-Theoretic Methods in Quantum Mechanics and Q…
Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH--KCBS scenario involving the entanglment of a qubit and a…
We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.
This paper is based on four assumptions: 1. Physical reality is made of linearly behaving components combined in non-linear ways. 2. Higher level behaviour emerges from this lower level structure. 3. The way the lower level elements behaves…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
Contemporary scientific perspectivism is re-evaluated and extended to a comprehensive perspectivist methodology and 'mediated' realistic epistemology, especially, with reference to quantum mechanics. In the present study, this is realized…
This paper provides a preparatory introduction to sheaves and topoi, written as a conceptual continuation of the author's earlier introduction to torsors and as preparatory background for the author's arXiv paper \emph{Grothendieck…
As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where…
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…
In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the…
Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer…
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and…
Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result the quantumness of nonentangled states has typically been overlooked and unrecognized. We give a robust definition for the…
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…
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…