Abstract The mixedness of the $N$-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix (RDM), which can describe the mixedness, is completely determined by the expectation values $\langle S_z \rangle $ and $\langle S_\pm \rangle $ for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa--Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case ($J < 0)$, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter ${\it\Delta }> {\it\Delta }_{\rm c} $.
Received: 13 April 2008
Revised: 21 April 2008
Accepted manuscript online:
PACS:
03.67.Lx
(Quantum computation architectures and implementations)
Fund: Project
supported by the National Natural Science Foundation of China (Grant
No 10547008), Specialized Research Program of Education Bureau of
Shaanxi Province (Grant No 08JK434), and the Youth Foundation of
Xi'an Institute of Posts and Telecommunications (Grant No
ZL2008-11).
Cite this article:
Hu Ming-Liang(胡明亮) and Xi Xiao-Qiang(惠小强) Mixedness of the N-qubit states with exchange symmetry 2008 Chin. Phys. B 17 3559
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