C^(3)⊗C^(d)系统中的纠缠见证优化

Entanglement witness optimization in C^(3)⊗C^(d) system

利用纠缠见证的定义和算子半正定的充要条件,得到C^(3)⊗C^(d)量子系统中厄米算子(W)是纠缠见证的充要条件.把C^(3)⊗C^(d)中W表示为分块矩阵,利用子块之间的关系,得到对任意可分态(ρ_(sep)),W是正算子的充要条件.对纠缠见证进行非线性改进,得到仅对部分可观测量进行测量,便能判别量子态是否纠缠的条件,并用例子验证,非线性改进后的纠缠见证能够判别出更多的纠缠态,优于其他文献中的纠缠见证.

Using the definition of entanglement witness and the necessary and sufficient condition of positive semi-definite operator,we present the necessary and sufficient condition for the Hermitian operator(W)to be the entanglement witness in the C^(3)⊗C^(d) quantum systems.The Hermitian operator in C^(3)⊗C^(d) is represented as a block matrix,using the relationship of the sub-blocks,the necessary and sufficient conditions of W to be a positive operator is obtained for any separable state(ρ_(sep)).Then the entanglement witness is improved non-linearly,the conditions for determining whether the quantum state is entangled or not by measuring only a part of the observable is obtained.Moreover,use examples to verify that the nonlinearly improved entanglement witness can detect more entangled states,which is better than the entanglement witness in other studies.