Quantum Shannon theory in the presence of indefinite causal order

本项目福尔斯属于EPSRC量子技术研究主题，或更具体地说，属于量子光学和信息研究领域。传统上，量子信息（香农）理论中的信息传输一直在量子通信信道以确定的因果顺序运行的背景下进行研究。经典物理学中隐含着这种因果关系的确定顺序。然而，这一假设的放松已被证明与量子物理学一致，最近的研究还表明，它可以促进量子通信的显着优势。该项目的目的是研究在量子香农理论及其潜在应用中，使用以不确定因果顺序建立的量子信道的影响。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通道，通常不能传输信息，可以以一种允许信息传输的方式组合在替代因果顺序的量子叠加中。这个新的想法使量子通道，可以处理量子力学输入和输出的叠加，也可以在量子叠加本身中组合。这种通常不可能实现的信息传输为量子通信开辟了一种新范式的可能性，在这种范式中，通信信道以因果顺序的各种叠加方式运行。为了充分理解这种新范式的优点，必须计算与不确定因果顺序中的信道组合的信息传输相关的容量，并与确定因果顺序下的容量进行比较。这将是该项目的起点。这些研究需要新技术的发展，结合量子香农理论的标准方法与最近引入的框架来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，也可以使用范畴量子力学，其中最近的一篇论文将不定因果顺序纳入描述量子因果结构的框架。一旦建立了描述具有不定因果顺序的通道的框架，并且量化了它们提供的潜在优势，该项目可以采取几个方向之一。一种可能性是研究特定的量子通信任务，这些任务可以利用不确定的因果排序。另一个有趣的方向是考虑量子力学基础的不确定因果结构的含义。在信息公理化方法之后，因果公理及其后果可以在不确定因果顺序的明确可能性下重新审视。这可以与研究自然界中可能已经存在什么样的不确定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。这样的基础研究可能对量子引力理论的构建有重要意义，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;尽管如此，在实现不确定因果结构的实际潜力时，实验结果的实现是重要的。去年刚刚完成了实验性创建一个没有明确因果顺序的过程的第一步。该项目预计将涉及与维也纳大学菲利普·沃尔特研究小组的合作，该研究小组目前正在实施一项提案，即以不确定的因果顺序排列去极化通道的量子通信。其他潜在的合作者包括名古屋大学的Masahito Hayashi和苏黎世联邦理工学院的Yuxiang Yang

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