  Since John Bell formulated his paramount inequality for a pair of spin-$1/2$
particles, quantum mechanics has been confronted with the postulates of local
realism with various equivalent configurations. Current technology, with its
advanced manipulation and detection methods, allows to extend the Bell tests to
more complex structures. The aim of this work is to analyze a set of Bell
inequalities suitable for a possibly broad family of many-body systems with the
focus on bosonic qubits. We develop a method that allows for a step-by-step
study of the many-body Bell correlations, for instance among atoms forming a
two-mode Bose-Einstein condensate or between photons obtained from the
parametric-down conversion. The presented approach is valid both for cases of
fixed and non-fixed number of particles, hence it allows for a thorough
analysis of quantum correlations in a variety of many-body systems.
