Title: A diagrammatic language for the Causaloid framework Show Chinese title

Title: 因果框架的图示语言

Abstract: The Causaloid framework is an operational approach aimed to house both the radical aspects of General Relativity -- dynamic causal structure, and Quantum Theory -- indefiniteness, to provide a scaffolding that might be suitable for Quantum Gravity by providing a landscape of theories that allow for indefinite causal structure. One may consider it as a generalisation of generalised probability theories (or GPTs) where a priori regions are not assumed to have any given causal relationship, to incorporate the possibility of indefinite causal structure. Since its conception, there have been many advances in the field of indefinite causal structure mostly stemming from the work of Chiribella et al. on the quantum switch and supermaps and from Oreshkov et al. on causal inequalities and process matrices. These approaches have systems moving along wires and use Hilbert space structure. They violate the standard causality constraints of Quantum Theory and, in this sense, can be regarded as post-quantum. The Causaloid approach does not necessarily have systems moving along wires or Hilbert spaces. This is the first paper in a trilogy of papers aiming to close the gap between the Causaloid (that allows for GPTs) and post-quantum studies that employ Hilbert spaces. To do so in the present paper, we provide a diagrammatic language for the Causaloid framework along with new terminology for the three levels of physical compression (called Tomographic, Compositional, and Meta compression). Show Chinese abstract

Abstract: 因果体框架是一种操作性方法，旨在容纳广义相对论的激进方面——动态因果结构，以及量子理论的不确定性，以提供一个可能适合量子引力的支撑结构，通过提供允许不确定因果结构的理论景观。可以将其视为广义概率理论（或GPTs）的推广，在这种情况下，不假设先验区域有任何给定的因果关系，以包含不确定因果结构的可能性。自提出以来，不确定因果结构领域已经取得了许多进展，主要源于Chiribella等人关于量子开关和超映射的工作，以及Oreshkov等人关于因果不等式和过程矩阵的工作。这些方法中系统沿着导线移动并使用希尔伯特空间结构。它们违反了量子理论的标准因果约束，从这个意义上说，可以被视为后量子。因果体方法不一定有系统沿着导线或希尔伯特空间移动。这是三部曲论文中的第一篇，旨在弥合允许GPTs的因果体（Causaloid）与使用希尔伯特空间的后量子研究之间的差距。为了在本文中实现这一点，我们为因果体框架提供了一种图形语言，并为三个层次的物理压缩（称为层析压缩、组合压缩和元压缩）提供了新的术语。