Quantum mechanics most definitely exhibits holism, where the sum of all the parts doesn't necessarily add up to the whole. Say u is spin up and d is spin down, and 1 is particle 1 and 2 is particle 2. For a pair of entangled particles we have mathematically,
|S>=(|u1>|d2> - |d1>|u2>)/(2^0.5)
as the spin state.
So, deriving the state of particle 1 we get
|S1>=(|u1> -|d1>)/(2^0.5)
For particle 2:
|S2>=(|d2> - |u2>)/(2^0.5)
Getting the two-state system between |S1> and |S2> gives us
|S'>=(|u1> -|d1>)(|d2> - |u2>)/(2)
This is not the same as |S>, so we have some sort of holism from quantum mechanics from entanglement. There is a good, more detailed discussion about this in Chapter 8: Parts and Wholes of Quantum Ontology by Peter J. Lewis. Mr. Lewis gives a very good discussion on how we most likely have some sort of holism, and all the major, non-Copenhagen interpretations agree with this (Lewis discusses many worlds, Bohemian mechanics, and GRW theory and how they support holism).
So what bridges this gap between |S> and |S'>? Between expectations and the world we see? Well, it seems we cannot just ignore this question. Quantum mechanics is certainly right in its predictions, so the theory itself must be correct. While I tried to ponder other solutions, it seems there is only one way to answer our question: there is a God. Now how does this solve our question? Well, God can make the bridge between the parts together and the sum of our parts one, He can and must be that gap. It is God who has to really encompass the other part of the human universe and His universe, so He brings together all the "parts" and is the reason for a bigger sum.
I didn't intend for this to be a sermon of sorts, it just seems that an explanation for holism in quantum mechanics is an indicator of God. This seems logical, and no other explanation is possible to fathom. Thank you for reading!