Classification witness operator for the classification of different subclasses of three-qubit GHZ class

Abstract

It is well known that three-qubit system has two kind of inequivalent genuine entangled classes under stochastic local operation and classical communication (SLOCC). These classes are called as GHZ class and W class. GHZ class proved to be a very useful class for different quantum information processing task such as quantum teleportation, controlled quantum teleportation etc. In this work, we distribute pure three-qubit states from GHZ class into different subclasses denoted by $S_1$, $S_2$, $S_3$, $S_4$ and show that the three-qubit states either belong to $S_2$ or $S_3$ or $S_4$ may be more efficient than the three-qubit state belong to $S_1$. Thus, it is necessary to discriminate the states belong to $S_i,i=2,3,4$ and the state belong to $S_1$. To achieve this task, we have constructed different witness operators that can classify the subclasses $S_i,i=2,3,4$ from $S_1$. We have shown that the constructed witness operator can be decomposed into Pauli matrices and hence can be realized experimentally.