But exactly this is not the case, exactly this is the difference between classical physics and quantum physics. Classically you place one coin in each of the two boxes, heads in one, tails in the other. Nothing strange happens here, the outcome is determined when setting up the boxes. When you look in one of the box, you will see either heads or tails as determined by the setup. The other box will have the coin showing the opposing side, also determined by the setup.

The quantum case is very different. You again place one coin in each of the two boxes, again one heads and one tails, but this time the coins are constantly flipping. It is no longer predetermined whether you will get heads or tails and only when you look in one of the boxes does the coin in there stops flipping and you see either heads or tails. But more importantly the other coin stops flipping at the very same time so that you will see the opposing side when you look into the second box.

The correlation is in both cases established when the boxes are setup, the coins will always show opposing sides. The quantum cases of course also requires both coins flipping synchronously. But in the classical case the exact outcome is also established during the setup while in the quantum case the exact outcome is only established when one looks in the first box.