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.
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Jafarizadeh, M.A., Karimi, N., Sahlan, D.A. et al. Hierarchy of graph-diagonal states based on quantum discord and entanglement classification . Eur. Phys. J. D 71, 254 (2017). https://doi.org/10.1140/epjd/e2017-80242-3
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DOI: https://doi.org/10.1140/epjd/e2017-80242-3