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Communications in Theoretical Physics

Quantum Discord of Non-X State

Jing-Ying Yao, Yuli Dong, Shiqun Zhu

Published Jun 1, 2013• 3 citations
Publisher

Abstract

The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors and are perpendicularly oriented. The geometric objects of tetrahedron T and octahedron O are deformed. The level surfaces of constant discord are formed by three interaction "tubes" along three orthogonal directions. They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased. In the phase damping channel, the quantum discord keeps approximately a constant when the time increases.

DOI
10.1088/0253-6102/59/6/07

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The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors and are perpendicularly oriented. The geometric objects of tetrahedron T and octahedron O are deformed. The level surfaces of constant discord are formed by three interaction "tubes" along three orthogonal directions. They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased. In the phase damping channel, the quantum discord keeps approximately a constant when the time increases.
The level surfaces of geometric discord for a class of two-qubit non-X states are investigated when the Bloch vectors are in arbitrary directions. The level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogonal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may either totally disappear or the open tubes may become closed tubes when the Bloch vectors reach a critical value. In the generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when the parameter γ increases. In the phase damping channel, the freezing phenomenon of geometric discord also exists.
We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of XXX states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys. Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and structures of quantum discord.
We evaluate analytically the quantum discord for a large family of multiqubit states. It is interesting to note that the quantum discord of three qubits and five qubits is the same, as is the quantum discord of two qubits and six qubits. We discover that the quantum discord of this family of states can be classified into three categories. The level surfaces of the quantum discord in the three categories are shown through images. Furthermore, we investigated the dynamic behavior of quantum discord under decoherence. For the odd partite systems, we prove the frozen phenomenon of quantum discord does not exist under the phase flip channel, while it can be found in the even partite systems.