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

Complementarity, distillable secret key, and distillable entanglement