Entanglement and non-locality in quantum networks

量子网络理论已经被研究作为一个基本的兴趣话题，也因为它们在量子通信中的可行应用。最终目标是实现所谓的“量子互联网”，它可以在全球范围内实现安全通信，并为盲量子计算和时钟同步等其他应用提供平台。虽然小量子网络已经在实验上实现，但在这些设置中，更好地理解量子相关性的确切性质仍有很大的空间。特别是，表征可制备态的集合，量化当前的纠缠，以及理解非定域性的强度仍然是相当感兴趣的问题。迄今为止，这方面的工作仅限于相对较小和简单的网络，例如星形或三角形网络。概括和统一的结果可以直接用于量子网络的设计，也可以为纠缠和非局部相关的本质提供基本的见解。在过去的几十年里，量子非局部性的话题得到了广泛的研究。这产生了对量子力学作为一种理论的“怪异”的广泛见解，也导致了设备独立和自我测试的想法，它探索了在不相信设备的情况下的物理学。这可能具有深远的技术含义，因为它可以仅以最低的假设提供加密安全性。一个深刻的认识是，非局部性，这个基本和抽象的量，可能恰恰是实现这种安全通信的资源。将我们对非定域性的理解扩展到网络仍然是一个突出的挑战。关键的区别之一是假设各种来源彼此独立-这取代了标准非定域性设置中的自由意志假设。据推测，可能有新的非定域性形式尚未被发现，这只会出现在网络场景中。阐述和理解这些问题将加深我们对量子理论的理解，同时也为进一步的技术发展铺平道路。该博士项目计划以该领域最近的工作为基础。这可能包括在给定网络中为准备状态导出新的必要条件，或提出新的实验测试。学生将有机会接触到量子相关领域的各种主题和工具，包括纠缠见证、凸优化和半确定规划。对于这个领域的博士项目来说，这是一个及时的时刻：由于它的起步阶段，这个项目有很大的空间来成长和扩展到新的研究方向，同时也建立在丰富的工具和相关文献的基础上。在量子信息的相关领域和主题中也有灵活性和参与的潜力韦纳，斯蒂芬妮，大卫·埃尔库斯和罗纳德·汉森。“量子互联网：对未来道路的展望。”科学学报，36 (2),6412 (2018).[qhBrunner, Nicolas，等。“贝尔非定域性。”现代物理评论（2014）：419弗里茨,托拜厄斯。“超越贝尔定理：相关情景。”物理学报（自然科学版）14(2012):103001。

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.