Not the quantum part.
Anti-Matter is like if you have a sound wave, and you play the exact opposite sound wave, they cancel each other out, and there is no sound. Anti-matter is the exact opposite of matter, meaning that thier could be an antimatter you. There are theories of complete antimatter galaxies that could exist out there.
The trouble with creating anti-matter in a lab is that if you are to store it, it has to be in a vacuum with no contact with real matter. SO, it cannot touch the sides of the container.
In the beggining of time, 'nothing' was divided into matter and anti-matter. For some reason (they don't know) some anti-matter spontaneously changed to matter. The rest annihalted back out and what we are left with is the spontaneously changed antimatter, which is what we are made out of.