New derivation of Born's law and parameter estimation based on a relative state formulation

TL;DR

This paper derives Born's law without probability concepts using a relative state formulation and introduces a method for parameter estimation based on indirect measurement, providing a new perspective on quantum measurement.

Contribution

It presents a derivation of Born's law without probability and proposes a parameter estimation method within a relative state framework, clarifying quantum measurement features.

Findings

Born's law derived without probability concepts

Parameter estimation method based on indirect measurement

Provides a simple solution to the measurement problem

Abstract

Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an indirect measurement model. While Deutsch adopt a concept of rational decision-maker who introduces probability, we adopt a concept of statistician in our measurement model and clarifies the distinguished feature of quantum measurement. Like many worlds interpretation, our scenario gives a simple solution for problem of measurement.