一句话：提出线性量子进程演算 lqCCS，并细化操作语义以约束上下文，给出更符合量子理论的 barb 与上下文双相似性。
已有量子进程演算扩展在语法与行为语义上尚无公认标准，量子值的可观察性质也未按量子理论验证。本文提出异步线性量子 CCS（lqCCS），可视为 qCCS 的线性异步版本；线性与异步通信契合不可克隆定理，保证每个 qubit 恰好发送一次，明确哪些 qubit 与上下文交互。作者用 barb 与上下文研究双相似性，发现一般上下文的观察能力与量子理论不相容：它们能依赖量子值作非确定性移动却不测量。为此细化操作语义，禁止上下文作不可行的非确定性选择，得到更粗的双相似性。该语义将量子态不可区分性提升到进程分布，并保留基于经典信息的非确定性选择表达力，是首个满足这两条性质的语义。
Past years have seen the development of a few proposals for quantum extensions of process calculi. The rationale is clear: with the development of quantum communication protocols, there is a need to abstract and focus on the basic features of quantum concurrent systems, like CCS and CSP have done for their classical counterparts. So far, though, no accepted standard has emerged, neither for the syntax nor for the behavioural semantics. Indeed, the various proposals do not agree on what should be the observational properties of quantum values, and as a matter of fact, the soundness of such properties has never been validated against the prescriptions of quantum theory. To this aim, we introduce a new calculus, Linear Quantum CCS (lqCCS), and investigate the features of behavioural equivalences based on barbs and contexts. Our calculus can be thought of as an asynchronous, linear version of qCCS, which is in turn based on value-passing CCS. The combination of linearity and asynchronous communication fits well with the properties of quantum systems (e.g. the no-cloning theorem), since it ensures that each qubit is sent exactly once, precisely specifying which qubits of a process interact with the context. We exploit contexts to examine how bisimilarities relate to quantum theory. We show that the observational power of general contexts is incompatible with quantum theory: roughly, they can perform non-deterministic moves depending on quantum values without measuring (hence perturbing) them. Therefore, we refine the operational semantics in order to prevent contexts from performing unfeasible non-deterministic choices. This induces a coarser bisimilarity that better fits the quantum setting: ( i ) it lifts the indistinguishability of quantum states to the distributions of processes and, despite the additional constraints, ( i i ) it preserves the expressiveness of non-deterministic choices based on classical information. To the best of our knowledge, our semantics is the first one that satisfies the two properties above.
@article{paperbot2655,
title = {Quantum Bisimilarity via Barbs and Contexts: Curbing the Power of Non-deterministic Observers},
author = {Lorenzo Ceragioli and Fabio Gadducci and Giuseppe Lomurno and Gabriele Tedeschi},
journal = {Proceedings of the ACM on Programming Languages},
volume = {8},
number = {POPL},
year = {2024},
doi = {10.1145/3632885}
}