Poissonian twin-beam states and the effect of symmetrical photon subtraction in loss estimations

We have devised an experimentally realizable model generating twin beam states whose individual beam photon statistics are varied from thermal to Poissonian keeping the non-classical mode correlation intact. We have studied the usefulness of these states for loss measurement by considering three different estimators, comparing with the correlated thermal twin beam states generated from spontaneous parametric down conversion or four-wave mixing. We then incorporated the photon subtraction operation into the model and demonstrate their advantage in loss estimations with respect to un-subtracted states at both fixed squeezing and per photon exposure of the absorbing sample. For instance, at fixed squeezing, for two photon subtraction, up to three times advantage is found. In the latter case, albeit the advantage due to photon subtraction mostly subsides in standard regime, an unexpected result is that in some operating regimes the photon subtraction scheme can also give up to 20% advantage over the correlated Poisson beam result. We have also made a comparative study of these estimators for finding the best measurement for loss estimations. We present results for all the values of the model parameters changing the statistics of twin beam states from thermal to Poissonian.