Eur. Phys. J. D (2017) 71: 254
https://doi.org/10.1140/epjd/e2017-80242-3

Regular Article

Hierarchy of graph-diagonal states based on quantum discord and entanglement classification

¹ Department of Theoretical Physics and Astrophysics, Tabriz University, 51664 Tabriz, Iran
² Department of science, Farhangian University, 19989-63341 Tehran, Iran
³ Department of Physics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

^a e-mail: nakarimi@yahoo.com

Received: 8 April 2017
Received in final form: 21 June 2017
Published online: 17 October 2017

Abstract

For the relative entropy-based measure of quantum discord the key idea is to find the closest classical state (CCS) for a given state ρ, which is in general a more complicated problem. In this work, we study three and four qubit graph-diagonal states and give the explicit expressions of CCS for these states. Using the CCS, we compute the quantum discord of graph-diagonal states of three and four qubit systems and show that there is a hierarchy for the quantum discord of graph-diagonal states of any three and four qubit systems. Then we classify the entanglement of graph-diagonal states of three and four qubit systems and draw the hierarchy of entanglement of these graph-diagonal states. Finally, we compare the hierarchy of quantum discord and quantum entanglement of the these graph-diagonal states and show that the hierarchy of quantum entanglement is at least in equivalence of quantum discord.