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arXiv quant-ph/0005014quant-ph
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纠缠证人的优化

Optimization of entanglement witnesses

M. Lewenstein, B. Kraus, J. I. Cirac, P. Horodecki

摘要:

纠缠见证(EW)是一种可以检测纠缠态的算子。我们给出了这种算子是最优的,即以最优的方式检测纠缠态的充分必要条件。我们展示了如何优化一般EW,然后我们将我们的结果具体化的不可分解的,后者是那些可以检测到积极的部分转置纠缠态(PPTES)。我们还提出了一种方法来系统地构建和优化这最后一类算子的基础上存在的“边缘”PPTES,即违反范围可分性标准的状态[物理。A{ \bf 232},333(1997)]以极端的方式。这种方法也允许系统的建设不可分解的积极地图(PM)。我们的研究结果导致了一个新的充分条件纠缠的不可分解的EW和PM。最后,我们通过构造作用于$H=\C^2\otimes \C^4$的最优EW来说明我们的结果。相应的PM构成了PM的第一个例子,具有最小的“量子位”域,或者-等价地-最小的厄密共轭余域。

英文摘要:

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the non-decomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES). We also present a method to systematically construct and optimize this last class of operators based on the existence of ``edge'' PPTES, i.e. states that violate the range separability criterion [Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also permits the systematic construction of non-decomposable positive maps (PM). Our results lead to a novel sufficient condition for entanglement in terms of non-decomposable EW and PM. Finally, we illustrate our results by constructing optimal EW acting on $H=\C^2\otimes \C^4$. The corresponding PM constitute the first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal hermitian conjugate codomain.

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