"Quantum illumination using polarization-entangled photon pairs for enhanced object detection: comment": reply

The Comment (10.1364/OE.548099) is related to the theoretical model in our paper, Opt. Express32, 40150 (2024)10.1364/OE.531674, used to describe the experimental result. The role of coincidence counting in our experiment is central; it serves as a crucial post-selection mechanism to isolate the most likely entangled photon pairs even when a significant fraction of photons are lost in one arm. To model the experimentally obtained results, in the paper two theoretical approaches were presented to model the photon loss, one to detect the presence of object (using the constant S value we get even when coincidence photon counts rate reduce) and the other to estimate the reflectivity of the object (normalized S value change with decrease in coincidence rate with reflectivity η). From the Comment, we gather that the second approach we have used to model photon loss and post-select is incorrect. To make it clear and complete, we have extended the first approach of using the complete Kraus operator to describe the dynamics from which we can detect the object and also estimate the reflectivity of the object. It accurately captures the experimental construct and is consistent with the results obtained from the measurable quantities. The second approach, using Kraus like operator M, which is erroneous, will be redundant.