  Quantum Zeno effect shows that frequent observations can slow down or even
stop the unitary time evolution of an unstable quantum system. This effect can
also be regarded as a physical consequence of the the statistical
indistinguishability of neighboring quantum states. The accessibility of
quantum Zeno dynamics under unitary time evolution can be quantitatively
estimated by quantum Zeno time in terms of Fisher information. In this work, we
investigate the accessibility of quantum Zeno dynamics in quantum open systems
by calculating noisy Fisher information, in which a trace preserving and
completely positive map is assumed. We firstly study the consequences of
non-Markovian noise on quantum Zeno effect and give the exact forms of the
dissipative Fisher information and the quantum Zeno time. Then, for the
operator-sum representation, an achievable upper bound of the quantum Zeno time
is given with the help of the results in noisy quantum metrology. It is of
significance that the noise affecting the accuracy in the entanglement-enhanced
parameter estimation can conversely be favorable for the accessibility of
quantum Zeno dynamics of entangled states.
