We propose a measure of quantum efficiency of a multimode state of light that quantifies the amount of optical loss this state has experienced, and prove that this efficiency cannot increase in any linear-optical processing with destructive conditional measurements. Any loss that has affected a state can neither be removed nor redistributed so as to further increase the efficiency in higher-efficiency modes at the expense of lower-efficiency modes. This result eliminates the possibility of catalytically improving photon sources.
@article{arxiv.1010.6302,
title = {Preservation of loss in linear-optical processing},
author = {Dominic W. Berry and A. I. Lvovsky},
journal= {arXiv preprint arXiv:1010.6302},
year = {2015}
}