论文标题
从其可能的操作形式主义中重建量子理论
Reconstructing quantum theory from its possibilistic operational formalism
论文作者
论文摘要
从操作的角度来看，我们为量子现象开发了一种可能的语义形式主义。该语义系统基于制备过程与是/否测试之间的CHU二元性，目标空间是配备了信息解释的三值集合。为状态空间引入了一组基本的公理。这组基本的公理足以限制状态的空间为投射域。然后在此域结构中表征纯状态的子集。在指定了属性和测量的概念之后，我们探讨了测量和最小令人不安的测量值之间的兼容性概念。我们通过要求存在区分是/否测试的方案，这是在国家空间建立正交关系的必要条件，从而实现了域结构在国家空间上的表征。关于状态空间的最后一个要求将相应的投影域限制为正常汇编。然后在状态空间上定义正交关系，并研究其属性。配备了这种关系，纯状态的正闭子集的正式链自然而然地继承了希尔伯特晶格的结构。最后，该系统的对称性被描述为ChU形态的一般子类。我们证明，这些CHU对称性保留了最小令人不安的测量结果和状态之间的正交关系。这些对称性自然导致了在纯状态的正常锁定子集集中定义的希尔伯特晶格的正常形态。
We develop a possibilistic semantic formalism for quantum phenomena from an operational perspective. This semantic system is based on a Chu duality between preparation processes and yes/no tests, the target space being a three-valued set equipped with an informational interpretation. A basic set of axioms is introduced for the space of states. This basic set of axioms suffices to constrain the space of states to be a projective domain. The subset of pure states is then characterized within this domain structure. After having specified the notions of properties and measurements, we explore the notion of compatibility between measurements and of minimally disturbing measurements. We achieve the characterization of the domain structure on the space of states by requiring the existence of a scheme of discriminating yes/no tests, necessary condition for the construction of an orthogonality relation on the space of states. This last requirement about the space of states constrain the corresponding projective domain to be ortho-complemented. An orthogonality relation is then defined on the space of states and its properties are studied. Equipped with this relation, the ortho-poset of ortho-closed subsets of pure states inherits naturally a structure of Hilbert lattice. Finally, the symmetries of the system are characterized as a general subclass of Chu morphisms. We prove that these Chu symmetries preserve the class of minimally disturbing measurements and the orthogonality relation between states. These symmetries lead naturally to the ortho-morphisms of Hilbert lattice defined on the set of ortho-closed subsets of pure states.
