| Geometric Measure of Quantum Entanglement for Multipartite Mixed States |
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| Shenglong Hu,Liqun Qi,Yisheng Song,Guofeng Zhang. Geometric Measure of Quantum Entanglement for Multipartite Mixed States. International Journal of Software and Informatics, 2014,8(3-4):317~326 |
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| Fund:This work is sponsored by the Hong Kong Research Grant Council (Nos. PolyU 502510, 502111, 501212, 501913, and 531213), the National Natural Science Foundation of China (Nos. 11401428, 11171094, 11271112, 61262026, and 61374057) and NCET Programm of the Ministry of Education (NCET 13-0738), science and technology programm of Jiangxi Education Committee (LDJH12088). |
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| Abstract:The geometric measure of quantum entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with respect to the geometric measure by means of a system of equations. The entanglement eigenvalue
for a mixed state is introduced. And we show that, for a given mixed state, its nearest disentangled mixed state is associated with its entanglement eigenvalue. Two numerical examples are used to demonstrate the effectiveness of the proposed method. |
| keywords:quantum entanglement geometric measure optimization |
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