  In the framework of quantum thermodynamics preparing a quantum system in a
general state requires the consumption of two distinct resources, namely, work
and coherence. It has been shown that the work cost of preparing a quantum
state is determined by its free energy. Considering a similar setting, here we
determine the coherence cost of preparing a general state when there are no
restrictions on work consumption. More precisely, the coherence cost is defined
as the minimum rate of consumption of systems in a pure coherent state, that is
needed to prepare copies of the desired system. We show that the coherence cost
of any system is determined by its quantum Fisher information about the time
parameter, hence introducing a new operational interpretation of this central
quantity of quantum metrology. Our resource-theoretic approach also reveals a
previously unnoticed connection between two fundamental properties of quantum
Fisher information.
