Topics on Causal Structures in Quantum Theory

该项目属于EPSRC物理科学研究领域的福尔斯。它的目的是扩大的结果和思想在我的硕士论文中开发，研究的过程理论框架建模因果尊重和因果违反时空区域之间的相互作用的范畴结构。在过程理论量子力学框架有一个假设的不对称性，时间箭头的假设方向。然而，在广义相对论中，时空的结构被视为一个动力学变量，因此将量子力学水平从时间箭头的假设方向中解放出来是一项重要的任务。1949年，哥德尔提出了爱因斯坦广义相对论方程的一个解，该解承认了封闭的类时曲线（CTC）的存在，即时空中违反时间顺序的区域。这些解决方案被许多人认为是非物理的：在经典物理学中，CTC的存在强加了一些自相矛盾的约束。然而，原则上它们并不被科学考虑所排除[2]。事实上，大卫多伊奇已经提出，在量子力学的水平上，任何“经典”病理都不会发生。多伊奇在1991年的论文“封闭类时线附近的量子力学”[1]中使用了量子计算理论的方法来构建一个理论，该理论可以解释如果我们在一个“传统”量子电路中包含一个违反时序的区域，代表一个假设的CTC的存在，会发生什么。20年后，Seth Lloyd提出了一种不同的方法，试图解决多伊奇提出的优雅解决方案中的一些问题。劳埃德模型是基于一种现象（后选择隐形传态），这是特别适合使用的方法和方法提供的分类量子力学的分析。因此，该项目的目标之一将是将这两种方法转化为一种分类和过程理论环境。这将使我们能够构建一个正式的数学框架，将形式化的，否则往往过于话语分析的量子现象附近的CTC和悖论所描述的两位作者。此外，我们可以尝试建立在Coecke和Kissinger发展的过程理论中的因果关系理论，看看在考虑CTC存在的同时，因果理论的想法可以在哪里以及如何保留。一个特别有前途的方面在于，多伊奇和劳埃德[1，2]开发的模型是相互不兼容的，然而，劳埃德并没有设法排除旧模型的物理性。一个组成和分类的方法的现象应该阐明这方面，甚至可以让我们排除两个模型之一，更重要的是构建一个可能的替代从组成的观察。该项目的主要优势之一在于方法的内在新奇，在上述论文[1，2]中，没有一个正式的设置，可以让我们谈论量子过程的因果结构，这实际上是由分类方法toquantum mechanics开发的工具提供的。参考书目[1]封闭类时线附近的量子力学-多伊奇，大卫物理学评论D44 3197-3217（1991）[2]时间旅行的量子力学通过后选择隐形传态-劳埃德等人。物理学评论D84 025007（2011）

This project falls within the EPSRC Physical Science research area. It is aimed at expanding the results and ideas developed in my master's thesis, which studied the categorical structure of a process theoretical framework modelling the interactions between causally respecting and causally violating regions of spacetime.In the process theoretical Quantum mechanical framework there is an assumed asymmetry, an assumed direction of the arrow of time. In general relativity the structure of the spacetime is however taken to be a dynamical variable, it is therefore an important task to free the quantum mechanical level from an assumed direction of the arrow of time. The project aims to develop a process theoretical framework which takes into account the possibility of local violations of the one-way time direction.In 1949, Godel proposed a solution to the Einstein's equations of general relativity which admits the existence of closed timelike curves (CTC), chronology-violating regions of the space time. Those solutions are by many considered to be unphysical: in classical physics the existence of the CTCs imposes some constraints which are paradoxical. However they are not in principle ruled out by scientific considerations [2]. In fact, it has been proposed by David Deutsch that at the level of quantum mechanics none of the 'classical' pathologies occur. Deutsch in the 1991 paper "Quantum mechanics near closed timelike lines" [1] uses the methods derived from the quantum theory of computation to construct a theory that would explain what happens if we include to a 'traditional' quantum circuit a chronology-violating region, representing the existence of an hypothetical CTC. Twenty years later Seth Lloyd proposed a different approach in an attempt to fix some problematic aspects of the otherwise elegant solution proposed by Deutsch [2]. Lloyd model is based on a phenomenon (post-selected teleportation) which is particularly amenable to an analysis using the methods and the approach provided by categorical quantum mechanics. One of the aims of the project will therefore be to translate the two approaches into a categorical and process theoretical setting. This will allow us to construct a formal mathematical framework which would formalise the otherwise often too discursive analysis of the quantum phenomena near CTCs and of the paradoxes described by the two authors. Moreover, we can try to build on the theory of causality in process theories developed by Coecke and Kissinger to see where and how the idea of a causal theory can be retained while taking into account the existence of CTCs. A particularly promising aspects lies in the fact that the models developed by Deutsch and Lloyd[1,2] are mutually incompatible, however, Lloyd doesn't manage to rule out the physicality of the older model. A compositional and categorical approach of the phenomena should shed light on this aspect and may even allow us to either rule out one of the two models and more importantly construct a possible alternative starting from compositional observations. One of the main strength of the project lies in the inherent novelty of the approach, in the above mentioned papers [1,2] there isn't a formal setting that would allow us to speak about the causal structure of quantum processes, this is in fact provided by the tools developed by the categorical approach toquantum mechanics.Bibliography[1] Quantum mechanics near closed timelike lines - Deutsch, David Phys. Rev. D44 3197-3217(1991)[2] The quantum mechanics of time travel through post-selected teleportation - Lloyd et al. Phys.Rev. D84 025007 (2011)