The notion of independence in crucial in algebraic quantum field theory: it expresses that local quantum systems pertaining to spacelike separated spacetime regions are causally independent. The talk reviews some notions of independence in the rich hierarchy of independence concepts and introduces the notions of operational independence and operational separability. Operational independence expresses that any two operations (understood as completely positive, unit preserving maps) on algebras associated with spacelike separated spacetime regions are co-possible; operational separability expresses that an operation carried out on a system does not cause a change in the sate of a spacelike separated system. The problem of status of operational independence and operational separability in the independence hierarchy is raised and some results and open problems are formulated.
LSE