Indeterminate Probabilities and the Weak Quantum Law of Large Numbers

TL;DR

This paper introduces a quantum law of large numbers for indeterminate probabilities, establishing a connection between ensemble theory and experimental relative frequencies through three theorems.

Contribution

It develops a new quantum probabilistic convergence concept for indeterminate probabilities, bridging theory and experiment with three foundational theorems.

Findings

Quantum probabilistic convergence derived for indeterminate probabilities.

Eigen-projector of the relative frequency operator linked to experimental relative frequency.

Formulation of the quantum probabilistic convergence as a key theoretical result.

Abstract

The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes the necessary bridge between ensemble theory and experiment. The second analyzes the most important theoretical ensemble entity: the eigen-projector of the relative frequency operator. Its physical meaning is the experimental relative frequency. The third theorem formulates the quantum probabilistic convergence, which is the final result of this investigation.