Entanglement and non-locality in quantum networks

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The theory of quantum networks has been studied both as a topic of fundamental interest, and also due to their viable application in quantum communications. The ultimate goal is of realising a so-called "quantum internet" [1] which could enable secure communication at a global level, as well as providing a platform for other applications such as blind quantum computing and clock synchronisation. Whilst small quantum networks are already experimentally achievable, there remains much scope to better understand the precise nature of quantum correlations in these settings. In particular, characterising the set of preparable states, quantifying the entanglement present, and understanding the strength of non-locality remain questions of considerable interest. Work in this area to date has been restricted to relatively small and simple networks, such as the star or triangle network. Generalisations and unifying results could directly feed into quantum network design, as well as providing fundamental insights into the nature of entanglement and non-local correlations.The topic of quantum non-locality has been studied extensively over the last few decades [2]. This has produced extensive insights into the "weirdness" of quantum mechanics as a theory, and also has led to the idea of device-independence and self-testing, which explores Physics when no trust of the devices is assumed. This may have profound technological implications, as it can provide cryptographic security with only the bare minimum assumptions. A profound realisation is that nonlocality, this fundamental and abstract quantity, could precisely be the resource enabling this secure communication.Extending our understanding of nonlocality to networks remains an outstanding challenge [3]. One of the key differences is to assume that the various sources are independent from one another - this replaces the assumption of free will in the standard nonlocality setting. It is conjectured that there may be new forms of nonlocality yet to be discovered, which only arise in network scenarios. Formulating and understanding these questions will deepen our understanding of quantum theory, whilst also paving the way for further technological development. This PhD project plans to build upon recent work in this area. This may include deriving new necessary conditions for preparing a state in a given network, or proposing new experimental tests. The student will have the opportunity to engage with a variety of topics and tools in the field of quantum correlations, including entanglement witnesses, convex optimisation, and semi-definite programming. It is a timely moment for a PhD project in this area: due to its infancy there is much room for this project to grow and expand into new research directions, whilst also building upon the wealth of tools and surrounding literature available. There is also potential for flexibility and engagement with related fields and topics within quantum information.[1] Wehner, Stephanie, David Elkouss, and Ronald Hanson. "Quantum internet: A vision for the road ahead." Science 362.6412 (2018).[2] Brunner, Nicolas, et al. "Bell nonlocality." Reviews of Modern Physics 86.2 (2014): 419.[3] Fritz, Tobias. "Beyond Bell's theorem: correlation scenarios." New Journal of Physics 14.10 (2012): 103001.