Resource theory of dephasing estimation in multiqubit systems

Abstract: 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.