  Estimation of physical parameters is a must in almost any part of science and
technology. The enhancement of the performances in this task, e.g., beating the
standard classical shot-noise limit, using available physical resources is a
major goal in metrology. Quantum metrology in closed systems has indicated that
entanglement in such systems may be a useful resource. However, it is not yet
fully understood whether in open quantum systems such enhancements may still
show up. Here, we consider a dissipative (open) quantum system of identical
particles in which a parameter of the open dynamics itself is to be estimated.
We employ a recently-developed dissipative quantum metrology framework, and
investigate whether the entanglement produced in the course of the dissipative
dynamics may help the estimation task. Specifically, we show that even in a
Markovian dynamics, in which states become less distinguishable in time, at
small enough times entanglement generated by the dynamics may offer some
advantage over the classical shot-noise limit.
