Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states

TL;DR

This paper derives formulas for entanglement and quantum discord in superpositions of GHZ and W states, revealing differences in their classical correlations and proposing a conjecture for W states.

Contribution

It provides explicit analytic expressions for entanglement and discord in superpositions of GHZ and W states, highlighting their distinct classical correlation properties.

Findings

Derived analytic entanglement measures for superposed GHZ and W states.

Presented explicit quantum discord formulas for these states.

Conjectured discord for N-qubit W states as log2 N.

Abstract

We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two $N$-qubit canonical orthonormal Greenberger-Horne-Zeilinger ($GHZ$) states and the same for two $W$ states. In course of characterizing all kinds of nonclassical correlations, explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the $GHZ$ state, the closest separable state to the $W$ state is not classical. Therefore, in this case the discord is different from the relative entropy of entanglement. We conjecture that the discord for the $N$-qubit $W$ state is $\log_2N$.