Exploring quantum enhancements from indefinite causality and time-reversing gates

事件发生在确定的因果顺序中，一个事件在时间上跟随另一个事件，这一概念是我们对我们所生活的古典世界的理解所固有的。然而，量子力学的定律允许放松对确定因果顺序的严格假设，从而产生因果顺序不确定的事件，这些事件是由因果顺序过程的量子叠加产生的[1]。不确定的因果关系可以被利用来实现量子计算[2]，量子通信[3，4]，量子计量学[5]和其他信息处理任务[6]的优势。它也对量子理论的基础和量子引力的概念有影响。该项目的目的是研究不确定因果关系的基本概念，并探索在理论和实验方面可以利用的潜在新量子优势。在这个混合项目中，我将首先致力于（i）制定能够违反所谓的“因果不等式”的物理过程的理论方面[7]（事件之间的相关性的界限，只要这些事件发生在一个明确的因果顺序中），以及（ii）可以从不确定的因果关系中实现的理论优势，然后再使用集成光子学进行实验工作。在实验方面，我将进行实验来说明量子计量学中不确定因果关系的优势，使用已经制造的硅光子芯片，现在可以进行表征。基于该项目第一阶段（理论）的结果，该项目还可能包括第一个原型实验，证明违反因果不等式或涉及四方的不确定因果顺序过程。除了不定因果关系的工作，我还将研究一个概念上相关的概念，即时间反转未知酉运算的可能性[8，9]及其在量子技术中的应用。我将扩展我在项目A中开始的理论工作，以实现一个协议，沿着施加酉噪声的信道无噪声地执行量子密钥分发（QKD）。我还将设计一个片上实验来演示参考文献[8，9]中的协议。

The notion that events happen in defined causal orders, where one event temporally follows another, is innate to our understanding of the classical world we live in. However, the laws of quantum mechanics allow the strict assumption of a definite causal order to be relaxed, giving rise to events with indefinite causal orders arising from quantum superpositions of causally ordered processes [1]. Indefinite causality can be exploited to achieve advantages in quantum computation [2], quantum communication [3,4], quantum metrology [5], and other information processing tasks [6]. It also has implications for the foundations of quantum theory and concepts in quantum gravity. The aim of this project is to investigate the fundamental concepts underlying indefinite causality and explore potential new quantum advantages that can be harnessed, both on theoretical and experimental fronts. In this hybrid project, I will first work on (i) the theoretical aspect of formulating physical processes able to violate so called "causal inequalities" [7] (bounds on the correlations between events which hold whenever these take place in a well-defined causal order), and (ii) theoretical advantages that can be achieved from indefinite causality, before moving onto experimental work using integrated photonics. On the experimental side, I will perform experiments to illustrate the advantage of indefinite causality in quantum metrology, using a silicon photonic chip that has already been fabricated and is now ready for characterisation. Based on the results obtained in the first (theoretical) phase of this project, this project may also include first prototype experiments demonstrating the violation of causal inequalities, or indefinite causal order processes involving 4 parties. Alongside the work on indefinite causality, I will also study a conceptually related concept, namely, the possibility of temporally reversing unknown unitary operations [8,9] and its applications for quantum technologies. I will extend the theoretical work I started in Project A for a protocol to perform quantum key distribution (QKD) noiselessly along a channel that applies unitary noise. I will also design an on-chip experiment to demonstrate the protocols in Ref. [8,9].