伯克霍夫-冯·诺依曼量子逻辑作为量子程序的断言语言

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Acta Informatica Pub Date : 2024-12-12 DOI:10.1007/s00236-024-00472-w

Shengyang Zhong

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引用次数: 0

摘要

在本文中，我们研究了在Ying （Birkhoff-von Neumann量子逻辑作为量子程序的断言语言，2022）中提出的带有纠缠量词的Birkhoff-von Neumann量子逻辑的稍微简化版本。arXiv: 2205.01959)。主要的结果是一个巧合定理，它说每个公式都是由希尔伯特空间中的一个封闭子空间来解释的，这个空间对应于公式的自由变量。我们还证明了在一阶逻辑中用于证明前范式定理的许多语义推论实例在该逻辑中也成立。技术工作是关于密度算子的张量积、支持和偏迹三种运算之间的相互作用。

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Birkhoff-von Neumann quantum logic as an assertion language for quantum programs

In this paper, we investigate a slightly simplified version of Birkhoff–von Neumann quantum logic enriched with entanglement quantifiers which is proposed in Ying (Birkhoff–von Neumann quantum logic as an assertion language for quantum programs, 2022. arXiv:2205.01959). The main result is a coincidence theorem, which says that every formula is interpreted by a closed subspace in the Hilbert space corresponding to the free variables of the formula. We also prove that many instances of semantic consequence, which are used in the proof of the prenex normal form theorem in first-order logic, also hold in this logic. The technical work is about the interplay among the three operations on density operators, namely, tensor product, support and partial trace.

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来源期刊

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.