Quantum causal modelling

背景、背景和影响经典因果模型通过提供一个可能产生统计相关性的因果结构来解释统计相关性。它们帮助我们回答了有关因果影响的本质以及因果影响模式对数据的约束的基本问题。它们具有广泛的实际应用，因为如果人们了解统计相关性背后的因果情况，就更有可能准确地预测未来干预措施中改变某些统计参数的结果。这对机器和人类一样适用，因此经典因果模型是人工智能和机器学习领域的一个关键话题。然而，人们早就知道，量子理论的范式特征（如“量子非定域性”）不能用经典标准给出因果解释。因此，近年来，在量子系统和设备的存在下，已经出现了各种因果建模方法的发展。该项目将开发专门为量子系统设计的新形式的因果建模。这对基础科学很重要，使我们能够回答有关量子宇宙中因果影响性质的基本问题，例如因果关系是否与代理人或参考框架有关，以及因果关系是否在时间上直接。这在实践中也很重要。一旦量子设备或设备网络变得比目前的小规模原型更大，设备的完整断层扫描就变得不可能了。这意味着，验证设备或网络的正常运行必须仅基于有限的数据。量子因果建模承诺一个明确的因果方法来验证的问题，其中的因果结构的设备或网络的推断是从有限的数据，然后用来预测未来的行为在不同的参数。这个项目福尔斯EPSRC物理科学和量子技术的研究领域。AimsThe项目是理论性的，不涉及实验或大规模计算。该项目的目标包括：（1）开发因果发现的新方法，能够区分经典设备产生的相关性和需要量子设备特殊排列的相关性。(2)描述可逆的因果结构（即，量子理论中的量子变换。(3)（更有野心。）从基本量子因果关系的网络中建立一个涌现时空模型。新颖的研究方法研究方法是跨学科的：该项目将结合联合收割机的见解和结果，从现有的文献经典因果模型与形式主义的量子信息理论。应用于上述目标的具体方法包括：（1）开发信息理论量，将熵和互信息的标准概念推广到彼此因果相关的量子系统（例如，在时间上是分开的）。(0)发展和使用新形式的图解符号。这将扩展现有的工作，使用范畴理论来描述量子过程，一个框架，是明确定制的表示量子因果结构。(2)以类似于现有作品的方式处理问题，这些作品从量子系统网络中建模涌现的空间关系，但扩展了方法，将空间和时间作为一个单一的实体。

Background, Context and ImpactClassical causal models give explanations of statistical correlations by providing a causal structure that could give rise to them. They have helped us to answer fundamental questions concerning the nature of causal influence, and the constraints that patterns of causal influence place on data. They have widespread practical application, since if one understands the causal situation underlying statistical correlations, one is more likely to accurately predict the result of changing some of the statistical parameters in future interventions. This applies to machines just as much as to humans, hence classical causal models are a key topic in the fields of AI and machine learning.However, it has long been known that paradigmatic features of quantum theory (such as `quantum nonlocality') cannot be given a causal explanation by classical standards. Hence recent years have seen the development of a variety of approaches to causal modelling in the presence of quantum systems and devices. The project will develop new forms of causal modelling designed specifically for quantum systems. This is of importance for fundamental science, enabling us to answer basic questions concerning the nature of causal influence in a quantum universe, such as whether causal relationships are relative to an agent or a reference frame, and whether causal relationships are directed in time. It is also practically important. Once quantum devices, or networks of devices, become larger than the current small-scale prototypes, full tomography of the device becomes impossible. This means that verification of the correct functioning of a device or network must be based only on limited data. Quantum causal modelling promises a distinctly causal approach to the problem of verification, wherein inferences about the causal structure of the device or network are made from limited data, and then used to predict future behaviour under different parameters.This project falls within the EPSRC Physical Sciences and Quantum Technologies research areas.AimsThe project is theoretical in nature, not involving experiment or large-scale computation. The aims of the project include:(1) Develop new methods for causal discovery, able to discriminate correlations produced by classical devices from those that require particular arrangements of quantum devices.(2) Characterize the causal structure of reversible (i.e., unitary) transformations in quantum theory.(3) (More ambitious.) Develop a model of emergent space-time from a network of fundamental quantum causal relationships. Novel research methodsThe research methodology is interdisciplinary: the project will combine insights and results from the existing literature on classical causal modelling with the formalism of quantum information theory. Specific methodologies applied to the aims above include:(1) Develop information theoretic quantities that generalise the standard notions of entropy and mutual information to quantum systems that are causally related to one another (e.g., are separated in time).(0) Develop and make use of new forms of diagrammatic notation. This will extend existing work that uses category theory to describe quantum processes, to a framework that is explicitly tailored for representing quantum causal structure.(2) Approach the problem in a similar manner to existing works, which model emergent spatial relations from a network of quantum systems, but extend the approach to include both space and time as a single entity.