Derivation of the quantum probability law from minimal non-demolition measurement

TL;DR

This paper derives the quantum probability law from the principle of minimal change in quantum non-demolition measurements, providing a new perspective on the fundamental law of quantum mechanics.

Contribution

It offers a novel derivation of the quantum probability rule based on the minimal change condition in ideal measurements.

Findings

Derivation of the Lueders formula from minimal change principles

Clarification of the connection between measurement and probability law

Insight into the foundational aspects of quantum measurement

Abstract

One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as ideal measurement, implies the probability law in a simple way. Namely, the very requirement of minimal change of state, put in proper mathematical form, gives the well known Lueders formula, which contains the probability rule.