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arXiv:1002.4124 · 物理学前沿：英文版

Quantum entanglement and disentanglement of multi-atom systems

Z. Ficek

Published Dec 2, 2009• 28 citations
arXivHTMLPDF
DOI
10.1007/s11467-009-0078-7

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In this paper, we present a scheme to prepare a set of the multi-atom entangled states by the cavity quantum electrodynamics (QED) technology. The multi-atom entangled states have some particular entanglement properties. For example, the remaining reduced density matrices ρ ij still retain entanglement or disentanglement when any N -2 atoms of the N atoms are traced out, which can be chosen freely according to our need and the relative entanglement strength of any pair of atoms (measured by the concurrence) can be arbitrarily adjusted. In addition, they may be completely symmetric under the exchange of any two atoms and perform certain quantum information tasks, such as telecloning, teleportation, secret sharing and so on.
We study the closest disentangled state to a given entangled state in any system (multi-party with any dimension). We obtain the set of equations the closest disentangled state must satisfy, and show that its reduction is strongly related to the extremal condition of the local filtering on each party. Although the equations we obtain are not still tractable, we find some sufficient conditions for which the closest disentangled state has the same reduction as the given entangled state. Further, we suggest a prescription to obtain a tight upper bound of the relative entropy of entanglement in two-qubit systems.
We show that, for a given entangled state in any system (multi-party with any dimension), the closest disentangled state always has the same reduction as the corresponding reduction of the given entangled state. This implies that any party cannot distinguish these two state without any classical communications. Furthermore, we determined 12 parameters in the Hilbert-Schmidt representation of the closest disentangled state in two qubits, and the minimization problem of the relative entropy of entanglement is reduced to the problem minimizing three parameters.