Entanglement is not a property about wave functions and really has nothing to do with waves. It's a logical consequence of the uncertainty principle and was ironically deduced by Einstein, Rosen, and Podolsky (EPR Paradox) as a way to argue that quantum mechanics is an incomplete description of physical reality. Being that it's strictly a consequence of the uncertainty principle, it applies equally well to non-wave function formulations of quantum mechanics such as the matrix formulation which does not use a wave function.
Entanglement is precisely the principle that a physical system can exist such that no part of the system can be described without describing the rest of the system as a whole. Einstein argued that this made quantum mechanics incomplete, the idea that somehow two properties of a physical system separated potentially by light years could not be decomposed into two physical systems that behaved independently of one another violated basic notions of local realism.
The issue is that as soon as you stated that one ball is red you have made a statement about some property of the physical system that is independent of the rest of the system. That is fundamentally what entanglement states you can not do. All you can state is that there are two balls that are in a superposition of being red and blue and there is no way to describe one ball as red and the other as blue, they are both red and blue simultaneously.
That is what entanglement is and that is the new principle that was neither known to the ancient Greeks or something that a 3 year old could figure out. Not the idea that if there are two balls and one ball is red and the other is blue, then if you see the red ball you know that the other ball is blue. Nothing about that ever baffled any physicist.