  In the last years, several works have demonstrated the advantage of photon
subtracted Gaussian states for various quantum optics and information
protocols. In most of these works, it was not clearly investigated the relation
between the advantages and the usual increasing energy of the quantum state
related to photon subtraction. In this paper, we study the performance of an
interferometer injected with multi photon annihilated squeezed vacuum states
mixed with coherent states for both single and correlated phase estimation. For
single phase estimation, albeit the use of multi-photon annihilated squeezed
vacuum states at low mean photons per mode provide advantage compared to
classical strategy, when the total input energies is held fixed, the advantage
due to photon subtraction is completely lost. However, for the correlated case
in analogous scenario, some advantage appears to come from both the energy rise
and improvement in photon statistics. In particular quantum enhanced
sensitivity with photon subtracted states appears more robust to losses,
showing an advantage of about 30% with respect to squeezed vacuum state in case
of realistic value of the detection efficiency.
