  We find an interesting relationship between multipartite bound entangled
states and the stabilizer formalism. We prove that if a set of commuting
operators from the generalized Pauli group on $n$ qudits satisfy certain
constraints, then the maximally mixed state over the subspace stabilized by
them is an unlockable bound entangled state. Moreover, the properties of this
state, such as symmetry under permutations of parties, undistillability and
unlockability, can be easily explained from the stabilizer formalism without
tedious calculation. In particular, the four-qubit Smolin state and its recent
generalization to even number of qubits can be viewed as special examples of
our results. Finally, we extend our results to arbitrary multipartite systems
in which the dimensions of all parties may be different.
