有限维二分量子可分性的计算
Computing finite-dimensional bipartite quantum separability
摘要：
自从纠缠被确定为一种计算和密码资源以来，人们一直在努力寻找一种有效的方法来判断给定的密度矩阵是否表示非纠缠或可分离的状态。本质上，这就是量子可分性问题。第1章至第3章提出了一种新的临界点算法，该算法在给定未知量子态的可观测量的正交基子集的期望值的情况下，在可观测量子集的范围内搜索纠缠见证。当所有期望值已知时，该算法解决了可分性问题。在第4章中，我给出了该算法的动机，并展示了如何在特定的物理场景中使用尽可能少的量子资源来检测未知量子态的纠缠（或确定可分性）。然后，我解释了算法背后的直观思想，并将其与同类标准算法联系起来。在本章的结尾，我将比较第3章中介绍的算法的复杂性。最后，在第5章中，我将详细介绍该算法，并讨论其相对于标准方法的性能。
英文摘要：
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. Chapters 1 to 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. When all the expected values are known, the algorithm solves the separability problem. In Chapter 4, I give the motivation for the algorithm and show how it can be used in a particular physical scenario to detect entanglement (or decide separability) of an unknown quantum state using as few quantum resources as possible. I then explain the intuitive idea behind the algorithm and relate it to the standard algorithms of its kind. I end the chapter with a comparison of the complexities of the algorithms surveyed in Chapter 3. Finally, in Chapter 5, I present the details of the algorithm and discuss its performance relative to standard methods.
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