Mixedness of the N-qubit states with exchange symmetry |
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Authors: | Hu Ming-Liang and Xi Xiao-Qiang |
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Institution: | Department of Applied Mathematics and Applied Physics,
Xi'an Institute of Posts and Telecommunications, Xi'an 710061,
China |
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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} $. |
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Keywords: | mixedness linear entropy symmetric quantum state |
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