Bounded information as a foundation for quantum theory

TL;DR

This paper proposes a foundational framework for quantum theory based on the principle that information in a physical system is inherently limited, using statistical and metric properties to reconstruct quantum mechanics.

Contribution

It introduces a novel approach to quantum reconstruction grounded in bounded information and measurement independence, linking statistical parameters to quantum structure.

Findings

Reconstruction of quantum linear and probabilistic structure

Framework based on metric properties of state space

Principle of measurement-independent information

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.