A new class of entanglement measures

TL;DR

This paper introduces a novel class of entanglement measures for quantum states, based on the greatest cross norm, satisfying key properties like convexity and invariance under local operations.

Contribution

It presents a new mathematical framework for quantifying entanglement using the greatest cross norm on trace class operators.

Findings

Measures satisfy convexity, invariance, and non-increase under local operations.

Provides a rigorous mathematical foundation for these entanglement measures.

Enhances understanding of entanglement quantification in quantum information theory.

Abstract

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.