What does Quantum Logic Explain?

Liang Liu

In this article,we describe the differences between classical logic gates and quantum logic gates,and explain the characteristics of quantum computation,the strong power of the quantum algorithm,and the problem of the realization of quantum logic gates.

S?awomir Bugajski

David J. Foulis, Charles H. Randall

Alexandru Baltag, Sonja Smets

In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the “dynamic turn” in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42:842–848, 1969 ), Piron (Foundations of Quantum Physics, 1976 ). By bringing these areas together we explain the basic ingredients of Dynamic Quantum Logic, a new direction of research in the logical foundations of physics.

Jonathan Kauffman

In this paper, the connections between classical propositional logic and Boolean algebras are explored. Then, an introduction to quantum logic explains that the distributive property does not hold, which gives rise to the need for a different structure for quantum logic. One of these systems, algebraic test spaces, is described, along with their connection to orthoalgebras, which are also analyzed.

Peter Mittelstaedt