A mathematical model for measurements in Quantum Mechanics

TL;DR

This paper introduces a simple mathematical model for quantum measurements that explains the Born rule and aligns with entanglement, using linear algebra and Hermitian operators.

Contribution

It presents a novel, straightforward model for quantum measurement that accounts for the Born rule and entanglement within a linear algebra framework.

Findings

The model reproduces the Born rule probabilities.

It demonstrates compatibility with entangled states.

Provides a clear mathematical framework for quantum measurements.

Abstract

Let $V=\mathbb{C}^N$, and $H$ (an observable) a Hermitian linear operator on $V$. Let $v_1,..., v_n$ be an orthonormal basis for $V$. Let $\mathcal{M}$ be a measurement apparatus prepared to measure a state of an observed system and collapses the state to one of the $v_j$'s. Here we propose a simple model which explains the Born rule and is compatible with entanglement.