Study on Quantum Discord in Mixed Three-Level States via Quantum Graph Scattering

Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee

M. A. Jafarizadeh, Naser Karimi, D. Amidi +2 more

Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee

This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corresponding to a diverse class of quantum states. To this effect, we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and call them graph Laplacian quantum states. We find the graph theoretic conditions for zero and nonzero quantum discord for these states. We apply these results on some important pure two qubit states, as well as a number of mixed quantum states, such as the Werner, Isotropic, and [Formula: see text]-states. We also consider graph Laplacian states corresponding to simple graphs as a special case.

Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee

In this paper we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and we call them graph Laplacian quantum states. Then we obtain structural properties of these graphs such that the corresponding graph Laplacian states have zero quantum discord by investigating structural properties of clustered graphs which provide a family of commuting normal matrices formed by the blocks of its Laplacian matrices. We apply these results on some important mixed quantum states, such as the Werner, Isotropic, and $X$-states.

Xiong Yang, Guo Hui Huang, Mao Fa Fang

Mohammed Daoud A, R. Ahl Laamara, S. Seddik

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system.Analytical expressions of geometric quantum discord are derived.A particular attention is devoted to two special classes of three-qubit X states.They include three-qubit states of W, GHZ and Bell type.We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.