Matter and antimatter annihilate each other to produce lots of energy. The same is true for protons and antiprotons. And since there are both proton and antiproton weapons present in the game, it would make sense for them to somehow work together for some additional effect, possibly in a similar way that assimilated tractor beam is boosted by kinetic cutting beam, or how expose powers allow the use of exploit powers. Something along the lines of leaving residual protons/antiprotons on the target, that cause micro explosions when the target is hit by the other weapon. Logically, it should work both ways, but since ap weapons deal enough damage as it is, perhaps it could be something benefiting the proton weapons instead.
IMO this would be a good way to boost existing proton-based weapons, or it could be a good basis for a potential new line of pure-protonic reputation weapons or something.
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http://memory-alpha.wikia.com/wiki/Antiproton