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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2506.18549 |
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| _version_ | 1866908432193290240 |
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| author | Ferro, Paolo |
| author_facet | Ferro, Paolo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded information as a foundation for quantum theory Ferro, Paolo Quantum Physics 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. |
| title | Bounded information as a foundation for quantum theory |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.18549 |