Entanglement and Mixed ness of Locally Cloned Non - Maximal W - State

Abstract

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W state or W - type state $|X>=\alpha|001>_{123}+\beta|010>_{123}+\gamma|100>_{123}, \alpha^{2} + \beta^{2} + \gamma^{2} = 1$ shared by three distant partners. Also we have considered the case $\beta=\gamma$, to obtain a range for $\alpha^2$, for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixed ness of inseparable states with their amount of inseparability, for that range of $\alpha^2$.