I'd even go so far as to say communism can't exist because it is fundamentally incompatible with the concept of property ownership.  They like to make the distinction between personal and private property, but this is a whimsical invention to back out of the corner they've painted themselves in.  The difference between the two is how resources are used, and, as you pointed out, the only way to deal with that would be to form a state with a police system.  Either that or mass violence to stamp out resistance.  Either way is garbage.