Concurrence for a two-qubits mixed state consisting of three pure states in the framework of SU(2) coherent states

TL;DR

This paper derives a simplified formula for concurrence in two-qubit mixed states with up to three non-zero eigenvalues, using SU(2) coherent states to analyze entanglement conditions.

Contribution

It introduces a new, simplified expression for concurrence applicable to certain mixed states and extends the analysis of entanglement using SU(2) coherent states.

Findings

Derived a simplified concurrence formula for specific mixed states

Established entanglement conditions in terms of coherent state parameters

Generalized the formalism to mixed states with up to three eigenvalues

Abstract

A simplified expression of concurrence for two-qubit mixed state having no more than three non-vanishing eigenvalues is obtained. Basing on SU(2) coherent states, the amount of entanglement of two-qubit pure states is studied and conditions for entanglement are calculated by formulating the measure in terms of some new parameters (amplitudes of coherent states). This formalism is generalized to the case of two-qubit mixed states using the simplified expression of concurrence.