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<p>The main purpose of this article is to study the lattice structure of quantum logics by using the theory of partially order sets. The goal is achieved by constructing a natural embedding map from the quantum logic posets into the complete lattices. The embedding map needs to be dense (in the order sense) and such complete lattices are so-called extended logics which preserve all essential features of the quantum logic. We obtain that the extended logic is unique up to a lattice isomorphism.</p>

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The Lattice Completion of Quantum Logic

  • 期刊论文

  • 发表日期：

    2025年6月15日

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  • Meixing Zhao,
  • Jinchuan Hou,
  • Kan He,
  • Feng Zhang

摘要

The main purpose of this article is to study the lattice structure of quantum logics by using the theory of partially order sets. The goal is achieved by constructing a natural embedding map from the quantum logic posets into the complete lattices. The embedding map needs to be dense (in the order sense) and such complete lattices are so-called extended logics which preserve all essential features of the quantum logic. We obtain that the extended logic is unique up to a lattice isomorphism.