Un-symmetric photon subtraction: a method for generating high photon number states and their relevance to loss estimation at ultimate quantum limit

We have studied theoretical un-symmetric multi-photon subtracted twin beam state and demonstrated a method for generating states that resembles to high photon number states with the increase in the number of subtracted photons through Wigner distribution function, which can be reconstructed experimentally by Homodyne measurement. A crucial point is high non-classicality is obtained by photon subtraction when mean photons per mode of twin beam state is low. We have calculated photon statistics from the phase space distribution function and found sub-poissonian behaviour in the same low mean photons regime. Furthermore, we have tested the usefulness of such states for realistic absorption measurement including detection losses by computing quantum Fisher-Information from measured Wigner function after interaction the sample. We have compared the performance of these states with respect to coherent and demonstrated how the quantum advantage is related to non-classical enhancement. We presented results up to three photon subtraction which show remarkable quantum advantage over both initial thermal and coherent state reaching the ultimate quantum limit in the loss estimation.