Entanglement and non-locality in quantum networks

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.

Our ambitions for the impact of the Quantum Engineering CDT are simple and clear: our PhD graduates will be the key talent that creates a new, thriving, globally-competitive quantum industry within the UK. In Bristol we will provide an entire ecosystem for innovation in quantum technologies (QT). Our strong and diverse research base includes strengths going from quantum foundations to algorithms, experimental quantum science to quantum hardware. What makes Bristol unique is our strong innovation and entrepreneurship focus that is deeply embedded in the entire culture of the CDT and beyond. This is reflected in our recent successful venture QTEC, the Quantum Technologies Enterprise Centre, and our Quantum Technologies Innovation Centre (QTIC), which are already enabling industry and entrepreneurs to set up their own QT activities in Bristol. This all occurs alongside internationally recognised incubators/accelerators SetSquared, EngineShed, and UnitDX.

At the centre of this ecosystem lies the CDT. We will not just be supplying existing industry with deeply trained talent, but they will become the CEOs and CTOs of new QT companies. We are already well along this path: 7 Bristol PhD students are currently involved in QT start-ups and 3 alumni have founded their own companies. We expect this number to rise significantly when the first CDT cohort graduates next year (2 students have already secured start-up positions). Equally, it is likely that our graduates will be the first quantum engineers to make new innovations in existing classical technology companies - this is an important aspect, as e.g. the existing photonics, aerospace and telecommunications industries will also need QT experts.

The portfolio of talent with which each CDT graduate will be equipped makes them uniquely suited to many roles in this future QT space. They will have a deep knowledge of their subject, having produced world-leading research, but will also understand how to turn basic science into a product. They will have worked with individuals in their cohort with very different skills background, making them invaluable to companies in the future who need these interdisciplinary team skills to bring about quantum innovations in their own companies. Such skills in teamworking, project management, and self-lead innovation are evidenced by the hugely successful Quantum Innovation Lab (QIL). The idea and development of QIL is entirely student-driven: it brings together diverse industrial partners such as Deutsche Bank, Hitachi, and MSquared Lasers, Airbus, BT, and Leonardo - the competition to take part in QIL shows the hunger by national industry for QT in general, and our students' skills and abilities specifically. With this in mind, our Programme has been co-developed with local, UK, and international companies which are presently investing in QT, such as Airbus, BT, Google, Heilbronn, Hitachi, HPE, IDQuantique, Keysight, Microsoft, Oxford Instruments, and Rigetti. The technologies we target should lead to products in the short and medium term, not just the longer term. The first UK-wide fibre-based quantum communication network will likely involve an academic-industrial partnership with our CDT graduates leading the way. Quantum sensing devices are likely to be the product of individual innovators within the CDT and supported by QTIC in the form of spin-outs. Our graduates will be well-positioned to contribute to the advancement of quantum simulation and computing hardware, as developed by e.g. our partners Google, Microsoft and Rigetti. New to the CDT will be enhanced training in quantum software: this is an area where the UK has a strong chance to play a key role. Our CDT graduates will be able to contribute to all aspects of the software stack required for first-generation quantum computers and simulators, the potential impact of which is shown by the current flurry of global activity in this area.