直觉主义视角下量子逻辑的进一步解释

Deeper Explanation of Quantum Logic in Intuitionistic Perspective

量子计算机将成为计算机科学未来的发展方向之一,量子逻辑是反映量子计算与量子信息的数学基础。Von Neumann用希尔伯特空间的闭子空间表示量子物理系统的性质,构成正交模格,其元素有明确的物理意义,但无法刻画叠加性质;Bob Coecke填加析取元素来表示叠加性质,借助Heyting代数,基于正交模格构造命题格对量子逻辑进行刻画,命题格中元素有明确的数学含义,但物理意义不够明确。针对后者,文中对命题格中元素的物理含义做出了进一步的解释,认为补充的析取元素代表的物理意义为描述叠加性质时所依赖的“观察者视角”,使得命题格中所有元素都获得了清晰的物理含义,通过阐述量子逻辑在测量时的应用,为量子计算中的隐形传态、超距同步等技术提供了重要的理论依据。

Quantum computer is becoming one of ongoing research direction of computer science.Quantum logic is the mathemati-cal foundation of quantum computation and quantum information.Von Neumann represented properties of quantum physical systems by closed subspaces of Hilbert space,thus constituting orthomodular lattice.Elements of orthomodular lattice own definite physical understanding but lack of the ability to describe superposition.Therefore,Bob Coecke constructed propositional lattice with Heyting algebra by adding disjunction elements for superposition.Elements of propositional lattice own definite mathematical meaning but lack of physical understanding.For latter,this paper gives a deeper explanation about physical understanding of elements of propositional lattice.As our viewpoint,the added disjunction elements represent“observer perspective”,which is required while depicting superposition in propositional lattice.Thus,by applying quantum logic on measurement operation,all elements of propositional lattice are given definite physical understanding and provide theoretical basis for quantum teleportation and action at distance.