  The Heisenberg limit is the superior precision available by entanglement
sensors. However, entanglementis fragile against dephasing, and there is no
known quantum metrology protocol that can achieve Heisenberg limited
sensitivity with the presence of independent dephasing. Here, we show that the
Heisenberg limit is attainable under the effect of independent dephasing under
conditions where the probe qubits decohere due to both target fields and local
environments. To detect the target fields, we exploit the entanglement
properties to decay much faster than the classical states due to collective
noise while most of the previous schemes use a coherent phase shift from the
target fields. Actually, if the temporally fluctuating target fields behave as
Markovian collective dephasing, we can estimate the collective dephasing rate
with a sensitivity at the Heisenberg limit under the effect of independent
dephasing. Our work opens the possibility for robust Heisenberg-limited
metrology.
