  We consider the many-body ground state of polarized fermions interacting via
zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We
rigorously prove that in the limit of infinite attractions spectral properties
of any-order reduced density matrix describing arbitrary subsystem are
completely independent of the shape of an external potential. It means that
quantum correlations between any two subsystems are in this limit insensitive
to the confinement. In addition, we show that the purity of these matrices
quantifying the amount of quantum correlations can be obtained analytically for
any number of particles without diagonalizing them. This observation may serve
as a rigorous benchmark for other models and methods describing strongly
interacting p-wave fermions.
