Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing, although atomicity is still commonly assumed, it has not been seriously studied, and a rigorous basis for it is missing. Classical results on atomicity do not directly carry over to distributed quantum computing, due to new challenges caused by quantum entanglement and the measurement problem from the underlying quantum mechanics. In this paper, we initiate the study of atomicity in distributed quantum computing. A formal model of (non-atomic) distributed quantum system is established. Based on the Dijkstra-Lamport condition, the system dynamics and observable dynamics of a distributed quantum system are defined, which correspond to the quantum state of and classically observable events in the system, respectively. Within this framework, we prove that local actions can be regarded as if they were atomic, up to the observable dynamics of the system.

翻译：原子性是分布式计算中普遍存在的假设，在此假设下，操作不可分割且呈现顺序性。在经典计算中，这一假设具有若干理论及实践保障。在量子计算中，尽管原子性仍被普遍假设，但尚未得到深入系统的研究，且缺乏严格的理论基础。由于量子纠缠及底层量子力学中的测量问题带来的新挑战，经典原子性结论无法直接适用于分布式量子计算。本文首次系统性研究分布式量子计算中的原子性，建立了（非原子）分布式量子系统的形式化模型。基于Dijkstra-Lamport条件，定义了分布式量子系统的系统动力学与观测动力学——分别对应系统中的量子态和经典可观测量事件。在此框架下，我们证明局部操作可视为具有原子性，且不影响系统的观测动力学。