Entanglement and nonlocality in quantum theory

2018年，我们完成了两个主要的研究项目。我们已经在两篇论文中写下了我们获得的结果：“逆转未知的量子变换：反转一般酉运算的通用协议”（提交给物理评论快报）和“实现具有多个输入状态副本的正映射”（提交给物理评论A）。关于量子酉操作的问题，我们对我们的量子算法进行了更深入的分析，这些算法将一个酉的多种用途转化为它的逆。我们找到了一种系统的方法来获得量子算法，用于转换量子酉运算的多个副本。这种系统的方法允许一种基于半确定规划的鲁棒数值方法，它可以在三类中找到最优协议：并行-输入副本可以同时使用-顺序-输入副本的使用以因果顺序的方式进行-以及一般-输入操作的使用可能不尊重明确的因果顺序。通过这种方法，我们证明了这三类之间存在着严格的层次关系，我们可以更好地理解具有不确定因果顺序的过程的力量和局限性。

In 2018 we have concluded our two main research projects. We have written the results we have obtained in two papers: “Reversing unknown quantum transformations: A universal protocol for inverting general unitary operations”, (submitted to Physical Review Letters) and “Implementing positive maps with multiple copies of an input state” (submitted to Physical Review A).Regarding the problem of quantum unitary operations, we made a deeper analysis into our quantum algorithms that transform multiple uses of a unitary into its inverse. We have found a systematic method to obtain quantum algorithms for transforming multiple copies of quantum unitary operations. This systematic method admits a robust numerical approach based in semi-definite programming which can find optimal protocols in in three classes: parallel - where the input copies can be used at the same time - sequential - where the use of the input copies are made in a causally ordered way - and general - where the use of the input operations may not respect a definite causal order. With this method, we have shown that there exists a strict hierarchy between these three classes and we could understand better the power and limitations of processes with indefinite causal order.