Exploring quantum enhancements from indefinite causality and time-reversing gates

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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].