Entanglement measurement based on convex hull properties

TL;DR

This paper introduces a novel entanglement measurement method based on convex hull properties, applicable to any quantum state dimension, addressing limitations of existing criteria.

Contribution

It proposes a new entanglement measurement scheme using convex hull analysis that works for all dimensions and state types, overcoming previous method restrictions.

Findings

Method applicable to any dimension and state fragment

Comparable results with existing entanglement metrics

Feasibility verified through multiple examples

Abstract

Quantum entanglement is a unique correlation phenomenon in quantum mechanics, and the measurement of quantum entanglement plays an important role in quantum computing and quantum communication. Many mainstream entanglement criteria and measurement methods currently known have shortcomings in certain aspects, such as not being sufficient or necessary conditions for entanglement, or only being effective in simple cases such as 2-qubits or pure states. In this work, we will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states, and analyzes the properties of the convex hull to obtain a new form of entanglement measurement. Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment. We will provide several examples to compare their results with other entanglement metrics and entanglement determination methods to verify their feasibility.