Entanglement and non-locality in quantum networks

量子网络理论既是一个基本的研究课题，也因为它在量子通信中的可行应用而受到研究。最终目标是实现所谓的“量子互联网”[1]，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一个平台。虽然小型量子网络已经可以在实验上实现，但在这些环境下，仍然有很大的空间来更好地理解量子关联的精确性质。特别是，表征一组可制备的态，量化存在的纠缠，以及理解非定域性的强度，仍然是相当感兴趣的问题。到目前为止，这一领域的工作仅限于相对较小和简单的网络，如星形或三角形网络。概括和统一的结果可以直接提供给量子网络设计，并提供对纠缠和非局域关联本质的基本见解。在过去的几十年里，量子非局域性的主题得到了广泛的研究[2]。这对量子力学作为一种理论的“怪诞”产生了广泛的见解，并导致了设备独立和自我测试的想法，即在假设不信任设备的情况下探索物理学。这可能具有深远的技术影响，因为它只需最低限度的假设即可提供加密安全性。一个深刻的认识是，非局域性，这个基本和抽象的量，可能恰恰是使这种安全通信成为可能的资源。将我们对非局域性的理解扩展到网络仍然是一个突出的挑战[3]。其中一个主要区别是假设各种来源彼此独立--这取代了标准非局部性设置中的自由意志假设。据推测，可能存在尚未发现的新形式的非局部性，这些形式仅在网络场景中出现。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。这个博士项目计划在这一领域最新工作的基础上再接再厉。这可能包括推导出在给定网络中准备状态的新的必要条件，或者提出新的实验测试。学生将有机会接触到量子关联领域的各种主题和工具，包括纠缠见证、凸优化和半定编程。现在是博士项目在这一领域的适时时刻：由于它还处于起步阶段，这个项目有很大的空间来发展和扩展到新的研究方向，同时也建立在丰富的工具和可用的周围文献的基础上。量子信息中的相关领域和主题也有灵活性和参与性的潜力。“量子互联网：未来道路的愿景。”《科学》362.6412(2018年)。[2]布鲁纳、尼古拉斯等人。“铃声非局部性。”《现代物理学评论》86.2(2014)：419.[3]托拜厄斯·弗里茨。“超越贝尔定理：相关场景。”《新物理学杂志》2012年10月刊103001期。

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.