Pairwise coexistence of effects versus coexistence

Abstract

Abstract The concept of coexistence of quantum mechanical effects is reviewed. We distinguish between coexistence and pairwise coexistence and give an example showing the non-equivalence the two concepts. A theorem on some closures of sets of pairwise coexistent effects is proved. Some proofs of the well-known fact that any set of pairwise coexistent (mutually compatible) sharp effects is coexistent are considered. In particular, a proof is presented that is based on the statement that every countably complete Boolean lattice of sharp effects is closed in some topology.