  We consider controllability of two conjugate observables Z and X by two
parties with classical communication. The ability is specified by two
alternative tasks, (i) agreement on Z and (ii) preparation of an eigenstate of
X with use of an extra communication channel. We prove that their feasibility
is equivalent to that of key distillation if the extra channel is quantum, and
to that of entanglement distillation if it is classical. This clarifies the
distinction between two entanglement measures, distillable key and distillable
entanglement.
