  Entanglement enhanced quantum metrology has been well investigated for
beating the standard quantum limit (SQL). However, the metrological advantage
of entangled states becomes much more elusive in the presence of noise. Under
strictly Markovian dephasing noise, the uncorrelated and maximally entangled
states achieve exactly the same measurement precision. However, it was
predicted that in a non-Markovian dephasing channel, the entangled probes can
recover their metrological advantage. Here, by using a highly controlled
photonic system, we simulate a non-Markovian dephasing channel fulfill the
quadratic decay behaviour. Under such a channel, we demonstrate the GHZ states
can surpass the SQL in a scaling manner, up to six photons. Since the quadratic
decay behavior is quite general for short time expansion in open quantum
systems (also known as the quantum Zeno effect), our results suggest a
universal and scalable method to beat the SQL in the real-word metrology tasks.
