论文标题
关于纠缠编号的一些评论
Some Remarks on the Entanglement Number
论文作者
论文摘要
古德（Gudder）在最近的一篇论文中定义了一种候选纠缠措施，该措施称为纠缠数字。纠缠编号首先是在纯状态下定义的，然后通过凸屋顶构造扩展到混合状态。在古德（Gudder）的文章中，这是一个空旷的问题，证明了最佳的纯状状态集合（OPSE）是从纯净到混合状态的纠缠数量的凸屋顶延伸。我们在肯定的问题上回答了古德的问题，因此我们得到纠缠数量仅在可分离状态下消失。更广泛地说，我们证明，在有限的尺寸希尔伯特空间的纯净状态下，任何功能的凸屋顶扩展存在。此外，我们通过使用Vidal在2000年开发的标准来证明纠缠数是LOCC单调的单调（以及纠缠度量）。我们提供了Vidal结果的简化证明，此外，我们在LOCC通信的情况下使用了有趣的树表示观点。最后，我们通过产生单调的纠缠措施家族来概括Gudder的纠缠数量，这些措施以自然的方式汇聚到纠缠的熵。
Gudder, in a recent paper, defined a candidate entanglement measure which is called the entanglement number. The entanglement number is first defined on pure states and then it extends to mixed states by the convex roof construction. In Gudder's article it was left as an open problem to show that Optimal Pure State Ensembles (OPSE) exist for the convex roof extension of the entanglement number from pure to mixed states. We answer Gudder's question in the affirmative, and therefore we obtain that the entanglement number vanishes only on the separable states. More generally we show that OPSE exist for the convex roof extension of any function that is norm continuous on the pure states of a finite dimensional Hilbert space. Further we prove that the entanglement number is an LOCC monotone, (and thus an entanglement measure), by using a criterion that was developed by Vidal in 2000. We present a simplified proof of Vidal's result where moreover we use an interesting point of view of tree representations for LOCC communications. Lastly, we generalize Gudder's entanglement number by producing a monotonic family of entanglement measures which converge in a natural way to the entropy of entanglement.
