  A correlational dialect is introduced within the quantum theory language to
give a unified treatment of finite-dimensional informational/operational
quantum theories, infinite-dimensional relativistic quantum theories, and
quantum gravity. Theories are written in terms of correlation diagrams which
specify correlation types and weights. Grouping similar correlation diagrams
leads to generalized Feynman diagrams, which in special cases reduce to the
familiar Feynman diagrams from quantum field theories. The correlational
formalism is applied in a study of correlation constraints, revealing new
classes of quantum processes that evade previous characterizations of general
quantum processes. The results apply to quantum theories of various kinds,
including time-asymmetric theories, time-symmetric theories, theories without
predefined time, and theories with indefinite causal structures.
