Which was helpful till now but there is no a priori reason that this must always be the case. And we might actually have reached to bottom in this regard with quantum physics where splitting things into pieces, studying them separately, and putting them together again does not really work anymore. A system of two or more quantum particles is not just the sum of those particles, the combined system can be in states that are not decomposable, i.e. the particles can be entangled.
Splitting the universe into galaxies, those into star systems, things in them into cells and molecules and then atoms and eventually elementary particles and all the success we had with this might give the impression that reductionism, that decomposing and reassembling things, is the only way that the world can be and that this will always work, but this is not true. And there is no a priori reason that the universe should be easily decomposable all the way down.
What do you mean with it? The quantum state of a two particle system? In that case I am pretty sure - even though I am not a physicist - that you are wrong. The quantum state of a two particle system can not be decomposed into two states, one state for each particle, in the general case. You can find the density matrix for each particle which will tell you how each corresponding particle will behave in isolation but you will lose information about the system by doing so in the general case.
Splitting the universe into galaxies, those into star systems, things in them into cells and molecules and then atoms and eventually elementary particles and all the success we had with this might give the impression that reductionism, that decomposing and reassembling things, is the only way that the world can be and that this will always work, but this is not true. And there is no a priori reason that the universe should be easily decomposable all the way down.