Entanglement of Bell Mixtures of Two Qubits

TL;DR

This paper derives algebraic formulas for entanglement measures of Werner states, a specific class of Bell mixture states, using theoretical methods to complement previous numerical results.

Contribution

It provides new algebraic formulas for entanglement measures of Werner states, enhancing understanding of their quantum entanglement properties.

Findings

Derived algebraic formulas for E_{pure} and E_{mixed} entanglements.

Identified optimal decompositions and entanglement operators for Werner states.

Confirmed and extended previous numerical results with algebraic derivations.

Abstract

This paper is an appendix to a previous paper: quant-ph/0101123 ``Relaxation Method for Calculating Quantum Entanglement", by Robert Tucci. For certain mixtures of Bell basis states, namely the Werner States, we use the theoretical machinery of our previous paper to derive algebraic formulas for: the pure and mixed minimization entanglements (i.e., E_{pure} and E_{mixed}), their optimal decompositions and their entanglement operators. This complements and corroborates some results that were obtained numerically but not algebraically in our previous paper. Some of the algebraic formulas presented here are new. Others were first derived using a different method by Bennett et al in quant-ph/9604024.