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

TL;DR

This paper develops specific witness operators to classify subclasses of three-qubit GHZ states, enabling experimental discrimination between different entanglement classes for quantum information tasks.

Contribution

The paper introduces new witness operators capable of distinguishing subclasses of GHZ states, facilitating experimental classification of three-qubit entanglement.

Findings

Witness operators can classify GHZ subclasses

Operators are decomposable into Pauli matrices

Experimental realization of classification is feasible

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.