{"title":"Birkhoff-von Neumann quantum logic as an assertion language for quantum programs","authors":"Shengyang Zhong","doi":"10.1007/s00236-024-00472-w","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"62 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-024-00472-w","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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