Preservation of loss in linear-optical processing

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.