Negative mass may actually be allowed by Einstein's theory of relativity. At least that is what a few proponents claim. Particles with negative mass are tachyons - which supposedly always travel faster than light. That does not mean they can carry positive information, but who knows - this topic is closer to SciFi than real Sci.
What is negative information? Interesting semantics - is factual information which is traveling at FTL best described negative info? which brings up the concept of "alternative facts" ... Maybe Kellyanne will be cured by same ...? Terry Blanton wrote: If information has mass, how can it travel FTL? https://www.discovermagazine.com/technology/the-quantum-internet-will-blow-your-mind-heres-what-it-will-look-like