AI 中文总结
本文基于2025年Ruiz等人的QRF形式体系，解决量子参考框架视角下子系统组合的悖论问题，建立QRF层级，刻画相容状态集，引入“经典化”程序恢复类经典视角，推广了标准量子理论的组合情况。
AI 中文摘要
通过组成部分理解复合系统是物理学中的基本实践。然而在量子参考框架（QRFs）语境中，将常规量子理论的组合概念与QRF视角结合会产生微妙问题，比如“第三个粒子悖论”。本文基于近期的QRF形式体系[Ruiz等人，2025年]深入研究QRF视角下子系统的组合方式：首先展示如何将外部观察者的框架内化并纳入该形式体系，从而建立一致的QRF视角层级，用于定义子系统的添加与移除；接着说明，由于所谓的“额外粒子”自由度，该形式体系能对子系统进行一致处理，从构造上避免任何悖论，且一致性意味着QRF视角下的子系统组合不同于并推广了标准量子理论的情况，具体而言，并非所有状态都能以张量积形式附加到QRF上，本文对相容状态集进行了刻画；最后，本文引入“经典化”程序，该程序可从一般QRF中恢复类经典视角，它规避了前述状态限制，但具有不同的操作意义，本文通过具体实例对其进行了研究。
英文摘要
Understanding a composite system through its constituents is a fundamental practice in physics. In the context of quantum reference frames (QRFs), however, combining the usual quantum-theoretic notion of composition with QRF perspectives gives rise to subtle issues, such as the 'paradox of the third particle'. Here we study in depth how to compose subsystems in QRF perspectives, building on a recent formalism for QRFs [E$.$Castro-Ruiz and O$.$Oreshkov, 2025]. We first show how the frames of external observers can be internalised and treated within the framework. This establishes a consistent hierarchy of QRF perspectives, which we use to define the adding and removing of subsystems. We then explain how, owing to the so-called 'extra-particle' degrees of freedom, the formalism gives a consistent treatment of subsystems, avoiding any paradoxes by construction. Consistency then implies that composing subsystems in a QRF perspective differs from, and generalises, the standard quantum-theoretic case. In particular, not every state can be appended in tensor-product form relative to a QRF, and we characterise the set of compatible states. Finally, we introduce 'classicalisation', a procedure that recovers a classical-like perspective from a general QRF. This procedure circumvents the aforementioned state restrictions but carries a different operational meaning, which we study through a concrete example.
Comments33 pages, 8 figures
