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Fundamenta Informaticae

Epistemic Quantum Computational Structures in a Hilbert-space Environment

Enrico G. Beltrametti, María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli

Published Jan 1, 2012• 20 citations
Publisher

Abstract

Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to i
DOI
10.3233/fi-2012-637

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In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

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Abstract Quantum information gives rise to some puzzling epistemic problems that can be interestingly investigated from a logical point of view. A characteristic example is represented by teleportation phenomena, where knowledge and actions of observers (epistemic agents) play a relevant role. By abstracting from teleportation, we propose a simplified semantics for a language that consists of two parts: 1)the quantum computational sub-language, whose sentences α represent pieces of quantum information (which are supposed to be stored by some quantum systems)2)the classical epistemic sub-language, whose atomic sentences have the following forms: agent a has a probabilistic information about the sentence α; agent a knows the sentence α. Interestingly enough, some conceptual difficulties of standard epistemic logics can be avoided in this framework.
Quantum mechanics predicts nature with extraordinary accuracy, yet it leaves one question unresolved: how do multiple possibilities become a single observed outcome? Logica Quanta: Logical Reasoning and the Formulation of Quantum Mechanics approaches this question through logical structure rather than interpretational preference. Instead of advocating for a particular interpretation, the work maps the finite set of logically admissible explanations—Many Worlds, stochastic collapse, epistemic models, hidden variables, superdeterminism, and physical collapse—and examines the conceptual cost associated with each. This book introduces a constraint-based framework built on two core tools: a Decision Tree that organizes the logical space of explanations, and a Cost Matrix that makes explicit what each approach preserves and sacrifices, including realism, determinism, explanatory completeness, and testability. Written from the perspective of a systems thinker with a background in financial markets, the work draws parallels between quantum measurement and complex-system transitions such as hysteresis, accumulation, and threshold-driven regime shifts. While not asserting equivalence between physics and economics, it highlights structural similarities in how systems evolve from possibility to outcome. A key argument developed in the book is that if collapse is a real physical process, its signatures may be difficult to isolate in macroscopic environments due to pervasive interference and rapid decoherence. This raises the possibility that lower-interference regimes, including controlled mesoscopic systems or space-based environments, may offer clearer conditions for testing collapse dynamics. The book does not claim to solve the measurement problem. Instead, it provides a logically structured map of the available explanatory landscape and invites skeptical examination of whether a physical, law-governed collapse mechanism—such as those explored within the Total Wave Modified Schrödinger Equation (TWMSE) framework—may remain a viable candidate after careful comparison of alternatives. This Zenodo entry accompanies the publication of the book and is intended as an accessible introduction to its conceptual foundations. 📘 Book link:https://a.co/d/0djmg6ZJ
Introduction Discussions of quantum-computational algorithms in the literature refer to various features of quantum mechanics as the source of the exponential speed-up relative to classical algorithms: superposition and entanglement, the fact that the state space of n bits is a space of 2 n states while the state space of n qubits is a space of 2 n dimensions, the possibility of computing all values of a function in a single computational step by “quantum parallelism,” or the possibility of an efficient implementation of the discrete quantum Fourier transform. Here I propose a different answer to the question posed in the title, in terms of the difference between classical logic and quantum logic, i.e., the difference between the Boolean classical event structure and the non-Boolean quantum event structure. In a nutshell, the ultimate source of the speed-up is the difference between a classical disjunction, which is true (or false) in virtue of the truth values of the disjuncts, and a quantum disjunction, which can be true (or false) even if none of the disjuncts is either true or false. In the following, I will discuss the information-processing in Deutsch's XOR algorithm (the first genuinely quantum algorithm) and related period-finding quantum algorithms (Simon's algorithm and Shor's factorization algorithm). It is well known that these algorithms can be formulated as solutions to a hidden-subgroup problem. Here the salient features of the information-processing are presented from the perspective of the way in which the algorithms exploit the non-Boolean logic represented by the projective geometry (the subspace structure) of Hilbert space.