A Note on the "Third Life of Quantum Logic"

Abstract

In the editor's introduction to the special volume "The third life of quantum logic: Quantum logic inspired by quantum computing" of this journal, Dunn, Moss, and Wang discussed the rôle of modular ortholattices. The present note is to provide some background for the results and problems mentioned there. In particular, we recall the two "limits" of subspace ortholattices of finite dimensional Hilbert spaces, the latter being structures related directly to quantum mechanics and quantum computation. These two "minimal" continuous geometries have been constructed by von Neumann and shown to be non-isomorphic.