Indefinite causal order as a resource for quantum technology

不确定因果顺序(ICO)描述的情况是，因果关系被打破，不再清楚，一个序列中的哪个事件或过程在另一个事件或过程之前。最近的基础研究已经开发出初步的理论协议，并实现了基于这样的ICO的第一次原理实验证明--其中序列中的事件既按顺序发生又以相反的顺序发生。虽然这些最初的演示是基本性质的，但ICO可能在量子通信、计量学和计算领域的技术进步方面拥有巨大的潜力。ICO是一个迅速崛起的概念，在很大程度上是在英国以外的地方发展起来的。此外，到目前为止，实验还很少，主要关注概念证明。然而，很明显，ICO为量子技术提供了一种替代资源，其优势预计可与量子纠缠提供的优势相媲美，有时甚至可能超过量子纠缠提供的优势。通过我们的网络，我们的目标是在英国研究人员和我们在欧盟及其他地区的国际同行的共同专业知识的基础上发展创新能力，他们是ICO领域的先驱。我们的网络将汇集研究人员，为量子技术应用提供关键实验技能和理论方法方面的丰富专业知识。这将使我们能够确定ICO最有前景的应用。我们将促进和促进与行业合作伙伴的联系，与相关利益攸关方一起探索ICO的用例和应用。这将使我们能够集中精力在回报最快的领域发展ICO。尽管存在潜在的技术优势，但使我们的世界观适应ICO构成了我们思维的范式转变--我们在因果推理链中接受培训和限制。我们的网络将提供一个平台来探索和挑战ICO的概念，特别是它与纠缠的关系，并在广泛的应用中测试它，受益于网络参与者提供的广泛专业知识。我们有意从有限数量的参与者开始，所有人都带来了探索并在可能的情况下应用这一新兴概念的强烈愿望。我们的核心参与者将在最有前途的实验平台上带来丰富的经验，包括高维光学、集成量子光学、光纤和波导、原子光学和纳米光子学，以及在量子逻辑、概率量子理论、量子信息和追溯方面的理论专业知识。根据我们的经验，合作的最佳方式是将正式的人际关系网与有共同兴趣的研究人员之间的大量个人联系结合起来。实现这一目标的机制包括每月举行研讨会、辅导、讨论和联网的虚拟会议、2个讲习班，以及最重要的是参与者之间的互访。我们提议的网络的主要目标是探索和量化ICO对第二次技术量子革命的优势，并确定将在中短期内受益于ICO的具体应用。我们对此持谨慎乐观态度，因为ICO是一种技术友好型资源。我们的长期愿景是将无限因果顺序的地位从一个有趣的概念概念提升到真正的量子资源，可以在开发适合第二次量子革命的技术时加以利用。

Indefinite causal order (ICO) describes situations, where causality is broken, where it is no longer clear, which event or process within a sequence preceded the other. Recent fundamental research has developed initial theoretical protocols and realised first proof of principle experiments that are based on such ICO - where events within a sequence are happening both in order and in reverse order. While these initial demonstrations are of a fundamental nature, ICO could hold tremendous potential for technological advances across quantum communication, metrology and computation. ICO is a rapidly emerging concept, which has been developed largely outside of the UK. Moreover, so far experiments are scarce and concerned mainly with conceptual proofs. It is clear, however, that ICO provides an alternative resource for quantum technologies, with advantages predicted to be comparable, and sometimes possibly surpassing, those offered by quantum entanglement.Through our network we aim to develop innovative competencies based on the joint expertise of UK researchers and our international colleagues in the EU and beyond, who have pioneered the field of ICO. Our network will bring together researchers offering a wealth of expertise in key experimental skills and theoretical approaches for quantum technological applications. This will allow us to identify the most promising applications for ICO. We will promote and facilitate links with industrial partners to explore use cases and applications around ICO with relevant stakeholders. This will allow us to concentrate our efforts on developing ICO in areas with the most immediate returns.Potential technological advantages notwithstanding, adapting our world view to ICO constitutes a paradigm shift in our thinking - we are trained and conditioned in causal chains of reasoning. Our network will provide a platform to explore and challenge the concept of ICO and specifically its relation to entanglement, and to test it on a broad range of applications, benefitting from the wide range of expertise provided by the network participants.We are deliberately starting with a limited number of participants, all bringing a keen desire to explore, and where possible apply, this emerging concept. Our core participants will bring a wealth of experiencein the most promising experimental platforms, including high-dimensional optics, integrated quantum optics, fibres and waveguides, atom optics and nanophotonics, as well as theoretical expertise in quantum logic, probabilistic quantum theory, quantum information and retrodiction. In our experience, collaborations work best by combining formal networking with a plethora of personal connections between researchers with joint interests. The mechanisms to achieve this include monthly virtual meetings for seminars, tutorials, discussions and networking, 2 workshops, and most importantly visits between participants. The main objective of our proposed network is to explore and quantify the advantages of ICO for the second technological quantum revolution, and to identify specific applications that would benefit from ICO in the short to medium term. We are cautiously optimistic about this because ICO is a technology-friendly resource. Our long-term vision is to boost the status of indefinite causal order from the level of an intriguing conceptual idea to that of a true quantum resource, that can be exploited in developing technologies fit for the second quantum revolution.