Bounded information as a foundation for quantum theory
- URL: http://arxiv.org/abs/2506.18549v2
- Date: Thu, 03 Jul 2025 16:19:27 GMT
- Title: Bounded information as a foundation for quantum theory
- Authors: Paolo Ferro,
- Abstract summary: This paper formalizes the concept that best synthesizes our intuitive understanding of quantum mechanics.<n>We introduce a second important hypothesis: if a measurement closely approximates an ideal one in terms of experimental precision, the information it provides about a physical system is independent of the measurement method.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of quantum theory. In our discussion, we also introduce a second important hypothesis: if a measurement closely approximates an ideal one in terms of experimental precision, the information it provides about a physical system is independent of the measurement method and, specifically, of the system's physical quantities being measured. This principle can be expressed in terms of metric properties of a manifold whose points represent the state of the system. These and other reasonable hypotheses provide the foundation for a framework of quantum reconstruction. The theory presented in this paper is based on a description of physical systems in terms of their statistical properties, specifically statistical parameters, and focuses on the study of estimators for these parameters. To achieve the goal of quantum reconstruction, a divide-and-conquer approach is employed, wherein the space of two discrete conjugate Hamiltonian variables is partitioned into a binary tree of nested sets. This approach naturally leads to the reconstruction of the linear and probabilistic structure of quantum mechanics.
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