Indefinite causal order as a resource for quantum technology

不确定因果顺序（ICO）描述了因果关系被打破的情况，在这种情况下，不再清楚序列中的哪个事件或过程先于另一个事件或过程。最近的基础研究已经开发了初步的理论协议，并实现了基于此类ICO的第一个原理实验证明-其中序列中的事件以顺序和反向顺序发生。虽然这些初步的演示是基础性的，但ICO可能在量子通信、计量和计算领域的技术进步方面具有巨大的潜力。ICO是一个迅速兴起的概念，主要是在英国以外发展起来的。此外，到目前为止，实验很少，而且主要涉及概念证明。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，我们的目标是基于英国研究人员和我们在欧盟及其他地区的国际同事的联合专业知识来开发创新能力，他们是ICO领域的先驱。我们的网络将汇集在量子技术应用的关键实验技能和理论方法方面提供丰富专业知识的研究人员。这将使我们能够确定ICO最有前途的应用。我们将促进和促进与行业合作伙伴的联系，与相关利益攸关方探讨ICO的用例和应用。这将使我们能够集中精力在最直接回报的领域开发ICO。尽管有潜在的技术优势，但让我们的世界观适应ICO构成了我们思维模式的转变——我们在因果推理链中受到训练和制约。我们的网络将提供一个平台，探索和挑战ICO的概念，特别是它与纠缠的关系，并在广泛的应用中对其进行测试，从网络参与者提供的广泛专业知识中受益。我们有意从数量有限的参与者开始，所有人都带着探索的强烈愿望，并在可能的情况下应用这一新兴概念。我们的核心参与者将带来高维光学、集成量子光学、光纤和波导、原子光学和纳米光子学等最有前途的实验平台的丰富经验，以及量子逻辑、概率量子理论、量子信息和回溯等方面的理论专业知识。根据我们的经验，通过将正式的网络与具有共同利益的研究人员之间的大量个人联系结合起来，合作的效果最好。实现这一目标的机制包括每月的研讨会、辅导课、讨论和网络、2个讲习班，以及最重要的参与者之间的访问。我们提出的网络的主要目标是探索和量化ICO在第二次技术量子革命中的优势，并确定在中短期内将受益于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不确定因果顺序的地位从一个有趣的概念想法提升到一个真正的量子资源，可以在开发适合第二次量子革命的技术中加以利用。

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.