Entanglement and nonlocality in quantum theory

2018年，我们完成了两个主要研究项目。我们已经把我们得到的结果写在两篇论文中：“反转未知的量子变换：用于反转一般酉运算的通用协议”，（提交给Physical Review Letters）和“使用输入状态的多个副本实现正映射”（提交给Physical Review A）.关于量子么正操作的问题，我们对我们的量子算法进行了更深入的分析，这些算法将酉的多次使用转换为它的逆。我们已经找到了一个系统的方法来获得量子算法转换多个副本的量子幺正操作。这种系统的方法承认一个强大的数值方法的基础上半定规划，可以找到最佳的协议在三类：并行-其中输入副本可以在同一时间使用-顺序-其中使用的输入副本是在因果顺序的方式-和一般-其中使用的输入操作可能不尊重一个明确的因果顺序。用这种方法，我们已经表明，这三类之间存在着严格的层次结构，我们可以更好地理解的权力和不确定的因果顺序的过程的限制。

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.