Advantages of the probability amplitude over the probability density in quantum mechanics

TL;DR

This paper explores the fundamental role of probability amplitudes in quantum mechanics, highlighting their advantages over probability densities in describing system dynamics and enabling nonlocal correlations through specialized information transfer experiments.

Contribution

The paper demonstrates that probability amplitudes offer unique benefits such as minimal error in codeword transfer, independence from coding parameters, and the ability to realize nonlocal correlations.

Findings

Probability amplitude leads to minimal transfer error.

Error is independent of coding parameters.

Enables realization of nonlocal correlations.

Abstract

We discuss reasons why a probability amplitude, which becomes a probability density after squaring, is considered as one of the most basic ingredients of quantum mechanics. First, the Heisenberg/Schrodinger equation, an equation of motion in quantum mechanics, describes a time evolution of the probability amplitude rather than of a probability density. There may be reasons why dynamics of a physical system are described by amplitude. In order to investigate one role of the probability amplitude in quantum mechanics, specialized codeword-transfer experiments are designed using classical information theory. Within this context, quantum mechanics based on probability amplitude provides the following: i) a minimum error of the codeword transfer; ii) this error is independent of coding parameters; and iii) nontrivial and nonlocal correlation can be realized. These are considered essential advantages of the probability amplitude over the probability density.