Constructions of quantum structures

Abstract

This chapter focuses on construction of quantum structures. Quantum structures essentially mean systems of events modeling abstract quantum mechanical experiments. These structures are equipped with the corresponding relations and operations derived from their interpretation. Depending on the assumptions, this chapter describes different levels of generality, from orthomodular lattices and orthomodular posets to orthoalgebras and effect algebras. It also illustrates common features of these structures, as well as their particular properties. Further, this chapter presents the contemporary techniques in a unified form. The most general quantum structures are the effect algebras, the orthoalgebras that are generally easier to understand. More specific quantum structures that include orthomodular posets and lattices are introduced as special types of orthoalgebras. Tools which are specific for quantum structures are also explored.