Acta Optica Sinica, Volume. 29, Issue 3, 827(2009)
Separability Condition for Multi-Mode Continuous-Variable Systems
A separability condition based on the product variance of a pair of Einstein-Podolsky-Rosen (EPR) type operators is obtained for continuous-variable systems by using Heisenberg uncertainty relation and Cauchy-Schwarz inequality. It can be used to detect the entanglement of non-Gaussian states, the entanglement of coherent state. Moreover, anther condition used to judge if quantum state gets entangled is obtained by using total variance. Two conditions were discussed contrastively were j was position operator, j was momentum operator and n=2. The result shows that detection ability of the former inequality is stronger than the latter when the coefficient is satisfied with the relatin of ∑|cjdj|>4.
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Pu Zhongsheng, Du Xiaofang, Gao Jianlong, Guan Qiuyun. Separability Condition for Multi-Mode Continuous-Variable Systems[J]. Acta Optica Sinica, 2009, 29(3): 827