Eliezer -

"Information" in this case is the properties; my apologies, I am loose with language. The properties were transformed - and, in the case of a splitting beam, with a 1-1 function. The properties were "lost" when they were split - they weren't the same as they were before. But they weren't irrecoverably lost. (At least close enough for testing; you may have medium degradation, i/e, property attenuation, depending upon the quality of the crystals and the intermediate material provided it isn't in a vacuum.)

To irrecoverably lose properties, you need a non 1-1 function - which is exactly what we had when we sent them through the filter rather than the splitter.