Mixed State Parametrization and Two-qubit Entanglement

TL;DR

This paper introduces a new parametrization scheme for mixed quantum states, specifically applied to two-qubit systems, enabling detailed analysis of entanglement properties using measures like negativity and concurrence.

Contribution

It presents a novel parametrization method for mixed states and applies it to analyze two-qubit entanglement, providing explicit results for specific state classes.

Findings

Explicit entanglement results for states with one parameter zero

Analysis of negativity and concurrence in 2-qubit states

New insights into mixed state entanglement structure

Abstract

A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our approach exploit much the interplay between is marked by pure states as Hilbert space vectors and mixed states as density matrices, both for the formulation of the parametrization and the analysis of entanglement properties. Explicit entanglement results, in terms of negativity and concurrence, for all 2-qubit mixed states with one single parameter/coordinate among the full set of fifteen being zero and a few other interesting cases are presented.