  We present a resource theory to investigate the power of a multqubit system
as a probe in the task of dephasing estimation. Our approach employs the
quantum Fisher information about the dephasing parameter as the resource
measure. Based on the monotonicity of quantum Fisher information, we propose
two sets of free operations in our resource theory, the Hamming distance
preserving operations and the selectively Hamming distance preserving
operations. We derive a necessary condition for the state transformation under
these free operations and demonstrate that uniform superposition states are the
golden states in our resource theory. We further compare our resource theory
with the resource theory of coherence and thoroughly investigate the relation
between their free operations in both single-qubit and multiqubit cases.
Additionally, for multiqubit systems, we discover the incompatibility between
the resource theory of dephasing estimation and that of $U(1)$ asymmetry, which
is responsible for phase estimation. The condition for enhancing the
performance of a probe state in phase estimation while preserving its ability
in dephasing estimation is also discussed. Our results provide new insights
into quantum parameter estimation by the resource-theoretic approach.
