  We show that the symmetry-restored paired mean-field states (quasiparticle
vacua) properly account for isoscalar versus isovector nuclear pairing
properties. Full particle-number, spin, and isospin symmetries are restored in
a simple SO(8) proton-neutron pairing model, and prospects to implement a
similar approach in a realistic setting are delineated. Our results show that,
provided all symmetries are restored, the pictures based on pair-condensate and
quartet-condensate wave functions represent equivalent ways of looking at the
physics of nuclear proton-neutron pairing.
