Sorry if this is a stupid question. My layman's understanding is that quantum mechanics describes the universe as a wave function, which can be understood as a weighted superposition (linear combination) of multidimensional sine waves (or equivalently, complex vectors) with particular frequencies and relative phases, and where the terms can be said to correspond to physically-valid "universes", weighted by complex probability amplitude. In general, one of the weird results is that when the phase matches precisely, the waves of different "universes" may cancel each other out, eg yielding an interference pattern in the two-slit experiment.
My vague intuition says that by some sort of symmetry in physical laws, for every such valid "universe", there should be some equivalent universe which is precisely identical except for sign, and which should thus cancel out. Of course this isn't expected to be the case locally in the presence of boundary conditions, but for the universe as a whole I'm not so sure.
Does my question make sense, or is it based on a fundamental misunderstanding? Are there particular asymmetries in our physical laws which break my intuition? Is this related to phenomena like matter/anti-matter asymmetry?