Quantum Shannon theory in the presence of indefinite causal order

这个项目属于EPSRC量子技术研究主题，或者更具体地说，属于量子光学和信息研究领域。传统上，量子信息中的信息传输(香农)理论是在量子通信通道按一定的因果顺序运行的背景下进行研究的。这种明确的因果顺序在经典物理学中是隐含的假设。然而，这一假设的放宽已被证明与量子物理一致，而且最近的研究表明，它可以促进量子通信中的显著优势。该项目的目的是研究在量子香农理论中使用不确定因果顺序设置的量子通道的效果及其潜在的应用。该项目的灵感来自于这一结果，表明两个完全相同的完全去极化的通道，通常不能传输信息，可以以一种确实允许信息传输的方式，以另一种因果顺序的量子叠加的方式组合在一起。这一新想法使可以处理量子力学输入和输出叠加的量子通道也可以组合成量子叠加本身。这种通常不可能实现的信息传输开启了量子通信中一种新范式的可能性，在量子通信中，通信通道以各种因果顺序的叠加方式运行。为了充分理解这种新范式的优势，必须计算与以不确定的因果顺序组合在一起的通道之间的信息传输相关的容量，并将其与在确定的因果顺序下发现的容量进行比较。这将是该项目的起点。这些研究需要开发新的技术，将量子香农理论的标准方法与最近引入的框架相结合，以描述不确定的因果结构。特别是，这些包括高阶映射的框架，以及过程矩阵，在范畴量子力学中也可以使用，其中最近的一篇论文将不确定的因果顺序纳入到描述量子因果结构的框架中。一旦建立了描述具有不确定因果顺序的通道的框架，并且它们提供的潜在优势被量化，该项目就可以采取几个方向中的一个。一种可能性是研究特定的量子通信任务，这可能利用不确定的因果顺序。另一个有趣的方向是考虑不确定因果结构对量子力学基础的影响。遵循信息公理的方法，因果公理及其后果可以用不确定的因果顺序的明确可能性来重新讨论。这可以与研究自然界中可能已经存在的那种不确定的因果结构，以及它们可以在什么样的物理机制中表现出来相结合。这种基础性研究可能对量子引力理论的构建具有重要意义，因为它结合了广义相对论的非固定因果结构和量子力学的概率特征。这是一个理论项目；然而，在未来实现不确定因果结构的实际潜力时，结果的实验实施是重要的。在实验中创造一个没有明确因果顺序的过程的第一步是在去年刚刚完成的。该项目预计将涉及与菲利普·沃尔特在维也纳大学的研究小组的合作，该小组目前正在实施这一提议，即通过以不确定的因果顺序安排的去极化信道进行量子通信。其他潜在的合作者包括名古屋大学的Masahito Hayashi和苏黎世ETH的杨宇翔

This project falls within the EPSRC Quantum Technologies research theme, or more specifically under the Quantum Optics and Information research area.Traditionally, information transfer in quantum information (Shannon) theory has been studied in the context of quantum communication channels operating in a definite causal order. Such definite ordering of causes and effects is implicitly assumed in classical physics. However, the relaxation of this assumption has been shown to be consistent with quantum physics, and recent research has moreover suggested that it can facilitate significant advantages in quantum communication The aim of the project is to investigate the effects of using quantum channels set up in an indefinite causal order within quantum Shannon theory and their potential applications. The project is inspired by the result, showing that two identical completely depolarising channels, which normally cannot transfer information, can be combined in a quantum superposition of alternative causal orders in a way that does allow information transfer. The novel idea enables quantum channels, which can process superpositions of quantum mechanical inputs and outputs, to also be combined in a quantum superposition themselves. Such information transfer where none would normally be possible opens up the possibility of a new paradigm in quantum communication, where communication channels are operated in various superpositions of causal orders.In order to fully understand the advantages of this new paradigm, the capacities associated with information transfer across channels combined in an indefinite causal order must be calculated and compared with those found under definite causal order. This will be the starting point of the project. These investigations require the development of new techniques, combining standard methods of quantum Shannon theory with more recent frameworks introduced to describe indefinite causal structures. In particular, these include theframeworks of higher order maps, as well as process matrices, developed in Categorical quantum mechanics could also be used, where a recent paper hasincorporated indefinite causal order into a framework for describing quantum causal structures.Once a framework has been established for describing channels with indefinite causal order and the potential advantages they provide quantified, the project may take one of several directions. One possibility is to investigate specific quantum communication tasks which could take advantage of indefinite causal orderings. Another interesting direction would be o consider the implications of indefinite causal structures for the foundations of quantummechanics. Following the informational axiomatic approach, the causality axiom and its consequences could be revisited with the explicit possibility of indefinite causal order. This could be combined with investigations into what sort of indefinite causal structures might already exists in nature, and in what sort of physical regimes they could manifest themselves. Such foundational research may have important implications in theconstruction of a theory of quantum gravity, as it combines a non-fixed causal structure from general relativity with probabilistic features of quantum mechanics. This is a theoretical project; nevertheless, experimental implementations of the results are important when going forward in realising the practical potential of indefinite causal structures. The first step to experimentally create a process without definite causal order was achieved just last year. This project is expected to involve collaboration with Philip Walter's research group at the University of Vienna, which is currently implementing the proposal, of quantum communication with depolarising channels arranged in an indefinite causal order. Other potential collaborators include Masahito Hayashi at Nagoya University and Yuxiang Yang at at ETH Zurich