Quantifying the entanglement of quantum states under the geometry method

TL;DR

This paper introduces new methods to quantify quantum entanglement using trace norms, providing analytical formulas for certain states and extending measures to tripartite systems.

Contribution

It proposes modified and extended entanglement measures based on trace norms, with analytical formulas for pure and two-qubit mixed states, and generalizes to tripartite states.

Findings

Analytical formula for pure states using modified measure

Analytical formula for two-qubit mixed states using extended measure

Generalization of the modified measure to tripartite states

Abstract

Quantifying entanglement is an important issue in quantum information theory. Here we consider the entanglement measures through the trace norm in terms of two methods, the modified measure and the extended measure for bipartite states. We present the analytical formula for the pure states in terms of the modified measure and the mixed states of two-qubit systems for the extended measure. We also generalize the modified measure from bipartite states to tripartite states.