Single-phase and correlated-phase estimation with multiphoton annihilated squeezed vacuum states: An energy-balancing scenario

In recent years, several works have demonstrated the advantage of photon-subtracted Gaussian states for various quantum optics and information protocols. In most of these works, the relation between the advantages and the usual increasing energy of the quantum state related to photon subtraction was not clearly investigated. In this paper, we study the performance of an interferometer injected with multiphoton-annihilated squeezed vacuum states mixed with coherent states for both single- and correlated-phase estimations. For single-phase estimation, although the use of multiphoton-annihilated squeezed vacuum states at low mean photons per mode provides an advantage compared to classical strategy, when the total input energy is held fixed, the advantage due to photon subtraction is completely lost. However, for the correlated case in the 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 the squeezed vacuum state in the case of a realistic value of the detection efficiency.