Does information have mass?

So this is a question I've been thinking about a lot lately. Due to this experiment that is going to attempt to measure the excess mass released from a carefully contained matter/anti-matter annihilation event. Or at least this is the proposal to measure the mass of information. The paper makes a case for information as a fifth state of matter, but I'm not exactly sure that is what it will prove at all. When I think of the outcome of a discovery such as information does indeed have mass, I think more along the lines of "Is this the most fundamental building block of matter?"

I do this a lot. Speculate and let ideas and possibilities unfold in my mind. It may be metaphysics, but I enjoy it.

Such as does this lend credence to the idea of the universe as a simulation? Maybe, or maybe information is just a fundamental building block of everything. Sort of harking back to the neo-hermetic ideology of the all of the universe is mind. That information in a fundamental state is what everything is? What will a successful experiment like this prove, that the logoi has been found objectively and it's really really small and strange?

Is information going to be classified with the massless particles or is it going to be even stranger like the completely hypothetical particles? I don't know, and I kind of like not knowing or really even having a good grasp of what reaching such a measurement might mean.

As I read the proposal paper it seems like a result of one extra photon means we might have a measurement of information and mass can be derived from that result. Does this indicate a new state of matter or something more fundamental than that? I don't know, but I hope someone finds out.