A four-party unlockable bound-entangled state

I present a four-party unlockable bound-entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, as either a determination of which Bell state is shared in the mixture, or as a kind of quantum teleportation with cancellation of Pauli operators.