信息--量子理论的基本概念

形式语言在观察概念中的表达限度

The Expressional Limits of Formal Languages in the Notion of Observation

在这篇文章中，我处理的概念，观察在最基本的意义上，其代表性的形式语言作为表达工具的形式公理理论。在这样做的时候，我在两个不同的背景下采用了这个概念。首先，它是一个认识论的概念，指的是它在形式数学环境中的解释，然后是它在量子力学环境中的解释。我试图探讨观察概念的第二个背景，是一种现象学的构成，基本上就像E。胡塞尔的原创作品假设在现象学构造中数学对象是知觉对象的特殊情况，因而也包括量子力学测量的对象，那么问题就在于探究用形式公理化理论的语言来描述它们的限度。一方面，我推导出一种不可还原的可观察物，作为不可分解的原子，在形式表征中没有任何进一步的句法内容;另一方面，我推导出一种超越性的连续底层，它自我构成为一种不可断言的合成统一体，在这种统一体上定义一个观察框架，并生成一个谓词性的话语宇宙。

量子计算复杂性

Quantum Computational Complexity

本文综述了量子计算复杂性，重点关注三个基本概念：多项式时间量子计算，量子证明的有效验证和量子交互式证明系统。基于这些概念，如BQP，QMA和QIP的量子复杂性类的性质。量子复杂性的其他主题，包括量子咨询，空间有界量子计算，和有界深度的量子线路，也进行了讨论。

量子信息基础

Fundamentals of Quantum Information Theory

本文介绍了量子信息理论的概念和数学基础。第一部分介绍了纠缠、通道、隐形传态等基本概念及其数学描述。第二部分着重介绍了该理论的定量方面。在这方面讨论的主题包括：纠缠措施，信道容量，两者之间的关系，可加性和连续性的性质和量子操作的渐近速率。最后，我们给出了一些最近的发展和开放的问题的概述。

Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling

In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix programme has correctly identified a notion of 'causal order' which plays an important role in fundamental physics, but this notion is weaker than the common-sense conception of causation because it does not involve asymmetry. We argue that causal order plays an important role in grounding more familiar causal phenomena. Then we apply these conclusions to the…

Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps

We analyze the relation between CP-divisibility and the lack of information backflow for an arbitrary -- not necessarily invertible -- dynamical map. It is well known that CP-divisibility always implies lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this letter it is shown that for a map which is not invertible the lack of information backflow always implies the existence of completely positive (CP) propagator which, however, needs not be trace-preserving. Interestingly, for a {\em wide class of image non-increasing dynamical maps} this propaga…

信息泛函与（不）确定性的概念：RMT -启发的案例

Information functionals and the notion of (un)certainty: RMT - inspired case

信息泛函允许量化给定概率分布的随机性程度，无论是绝对的（通过最小/最大熵原则）或相对于规定的参考。我们的主要目的是分析“最小信息”假设，这是一个经典的概念（R。Balian，1968）在随机矩阵理论中。我们把特别强调通用水平（特征值）的间距分布和它们的随机性，或者-信息/组织赤字的程度。

Entanglement, Complexity, and Causal Asymmetry in Quantum Theories

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry -- and thus of causation -- in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum systems. I show that by exploiting a connection between the amount of e…

Fundamentals of fractional revival in graphs

We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of vertices, and give various examples. This work resolves two open questions of Chan et.~al. ["Quantum Fractional Revival on graphs". Discrete Applied Math, 269:86-98, 2019.]

论量子态标准概念的物理不可维持性

On the Physical Untenability of the Standard Notion of Quantum State

本文揭示了由 Dirac 和 von Neumann 确立的量子力学标准解释（SQM）中量子态概念多种定义间的深层不一致性，指出这种混淆导致了主流文献中的自相矛盾，并论证了该概念对理论物理学理性理解的不可维持性。

量子测量、信息和熵的产生

Quantum Measurements, Information and Entropy Production

为了理解关于量子测量与热力学第二定律之间关系的Landau-Lifshitz猜想，我们讨论了量子物体对经典测量仪器施加的“绝热”力和“绝热”力的概念.该方法体现了测量中的热和功的概念，探讨了信息熵与热力学熵的关系。

Fundamental limits on information processing from black-hole thermodynamics

Thought experiments involving thermodynamic principles have often been used to derive fundamental physical limits to information processing and storage. Similar thought experiments involving black holes can shed further light into such limits.

Replacing the Notion of Spacetime Distance by the Notion of Correlation

Spacetime is conventionally viewed as a stage on which actors, in the form of fields, move. Here, we explore what may lie beyond this picture. The starting point is the observation that quantum fluctuations of fields are the more strongly correlated the shorter their spacetime distance. As a consequence, the notion of spacetime distance, including the metric as its infinitesimal version, can be replaced by the notion of correlation strength. This suggests a new picture in which abstract (2-point and multi-point) correlators are the primary structure. In general, these abstract correlators can …

量子空间是模的

Quantum Spaces are Modular

目前，我们的空间概念是一个经典的概念。考虑到量子理论比经典物理学更基本，空间应该被赋予一个纯粹的量子定义，我们从量子力学的角度重新审视欧几里得空间的概念。由于空间在物理学中是以相对论场或薛定谔波泛函的标记形式出现的，我们建议将欧几里得量子空间定义为量子理论的海森堡代数的极化选择。我们表明，以下麦基，一般来说，这样的偏振包含一个基本的长度尺度和相反的是暗示的薛定谔偏振，他们拥有拓扑不同的光谱。这些是模块化空间。我们表明，他们自然配备了额外的几何结构，通常遇到的背景下，弦论或广义几何。此外，我们展示了模块化空间如何调和存在的基本尺度与平移和旋转不变性。我们还讨论了当薛定谔空间是一个奇异极限时，通常的经典空间概念如何表现为模空间的一种极限形式。

交互式量子协议中的信息流：遗忘的代价

The Flow of Information in Interactive Quantum Protocols: the Cost of Forgetting

在两方交互量子通信协议的背景下，我们研究了最近定义的量子信息代价（QIC）的概念，它具有其经典类似物的大多数重要性质。虽然这个定义的优点是对完全量子输入和任务有效，但它对经典任务的解释仍然相当模糊。此外，这个新概念与以前出现在文献中的量子协议的其他信息成本概念之间的联系并不清楚，如果存在的话。我们解决这两个问题：对于具有经典输入的量子通信，我们提供了关于输入寄存器的信息的QIC的替代表征，避免了对经典输入状态的纯化的概念的任何引用。我们提供了一个确切的操作解释，这种替代表征的成本的总和，传输信息的经典输入和忘记这些输入的信息的成本。为了得到这个特征，我们证明了一个一般引理，信息流引理，准确地评估一般交互量子过程中的信息传递。通过对量子经典协议的模拟，进一步阐明了量子经典协议与量子信息中心之间的联系。最后，我们应用这些概念来论证，任何不忘记信息的量子协议都解决了Omega（n）通信中n比特的不相交性，完全失去了二次量子加速。这提供了一个特定的意义，其中遗忘信息是交互式量子协议的必要特征。我们还应用这些概念证明了QIC在零错误是正好为n的内积功能，和n（1 - o（1））的随机布尔函数的n+n位。