  Model-independent identities and inequalities relating the various spin
observables of a reaction are reviewed in a unified formalism, together with
their implications for dynamical models, their physical interpretation, and the
quantum aspects of the information carried by spins, in particular
entanglement. These constraints between observables can be obtained from the
explicit expression of the observables in terms of a set of amplitudes, a
non-trivial algebraic exercise which can be preceded by numerical simulation
with randomly chosen amplitudes, from anticommutation relations, or from the
requirement that any polarisation vector is less than unity. The most powerful
tool is the positivity of the density matrices describing the reaction or its
crossed channels, with a projection to single out correlations between two or
three observables. For the exclusive reactions, the cases of the
strangeness-exchange proton-antiproton scattering and the photoproduction of
pseudoscalar mesons are treated in some detail: all triples of observables are
constrained, and new results are presented for the allowed domains. The
positivity constraints for total cross-sections and single-particle inclusive
reactions are reviewed, with application to spin-dependent structure functions
and parton distributions. The corresponding inequalities are shown to be
preserved by the evolution equations of QCD.
