# A Theory of Entanglement

## TL;DR

This paper develops a foundational theory of quantum entanglement, introducing a new measure called the entanglement number, and explores its properties within bipartite systems, bridging classical and quantum perspectives.

## Contribution

It presents a novel theoretical framework for understanding entanglement, including a new entanglement measure, and integrates classical and quantum approaches.

## Key findings

- Introduces the entanglement number as a new measure.
- Links entanglement robustness with the entanglement number.
- Focuses on bipartite quantum systems.

## Abstract

This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert space in terms of context coefficients. In Section~3 we combine the work of the first two sections to develop a general theory of entanglement for quantum states. A measure of entanglement called the entanglement number is introduced. Although this number is related to entanglement robustness, its motivation is not the same and there are some differences. The present article only involves bipartite systems and we leave the study of multipartite systems for later work.