Multipartite Unlockable Bound Entanglement In The Stabilizer Formalism

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 [Smolin, Phys. Rev. A 63, 032306 (2001)] and its recent generalization to even numbers of qubits [Bandyopadhyay et al., Phys. Rev. A 71, 062317 (2005); Augusiak et al., ibid 73, 012318 (2006)] 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.