To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement measure is entanglement monotone and convex are presented, as well as the interpretation of smoothed one‐shot entanglement cost. Next, a difference between the measure under the local operation and classical communication and the separability‐preserving operations is presented. Then, the relation between the convex roof extended method and the way here for the entanglement measures built from the geometric entanglement measure for pure states, as well as the concurrence for pure states in two‐qubit systems are considered. It is also shown that the measure is monogamous for $2\otimes 2\otimes d$ system.

中文翻译：

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纯状态纠缠措施的扩展

量化纠缠是量子纠缠理论中最重要的主题之一。纠缠度是根据纯态度建立的。给出了纠缠度为纠缠单调和凸度时的条件，以及对平滑的单次纠缠代价的解释。接下来，介绍了本地操作和经典通信下的措施与可分离性保存操作之间的区别。然后，考虑了凸屋顶扩展方法与此处由纯态的几何纠缠度量建立的纠缠方法之间的关系，以及在两个量子位系统中纯态的并发性。还表明该措施是一夫一妻制$\mathrm{2个}\otimes \mathrm{2个}\otimes d$ 系统。