  We study the decay of bosonic many-body states in the three well Bose-Hubbard
chain where bosons in the central well can escape into a reservoir. For
vanishing inter-particle interaction this system supports a non-decaying
many-body state which is the antisymmetric Bose-Einstein condensate with
particles occupying only the edge wells. In the classical approach this quantum
state corresponds to a symmetry protected non-decaying state which is stable
even at finite interaction below a certain intensity threshold. Here we
demonstrate that despite the classical counterpart is stable the antisymmetric
Bose-Einstein condensate is always metastable at finite interatomic
interactions due to quantum fluctuations.
