Related papers: Use of Mathematical Logical Concepts in Quantum Me…
Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be…
A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the zeros in a product qubit state do not contribute to the number. They serve only as…
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Simple representations of documents based on the occurrences of terms are ubiquitous in areas like Information Retrieval, and also frequent in Natural Language Processing. In this work we propose a logical-probabilistic approach to the…
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by…
The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties…
Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise…
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…
The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
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…