Take a situation where we have (classical) uncertainty about a situation. For example, I toss a coin and hide the outcome from you. When I reveal it, nothing about the coin changes. The coin either landed heads or it landed tails. All that changed was your state of knowledge about the outcome. Nothing remarkable there.
Now, consider the quantum analogue of this example. The heads and tails become states of a qbit, for example. Let’s call it a quantum coin. When we measure the state, is it still the case that all that changed was our state of knowledge about the state? That the state was always either heads or tails?
It can’t be so simple. Let’s consider a second property of the coin, it’s colour. So it has two measurable properties: the face, which may be heads or tails, and the colour, which let’s say may be gold or silver. Crucially, the quantum coin can’t have a definite colour and a definite face simultaneously, whereas the classical coin can of course have a definite face showing and a definite colour. This is the important complication relative to the classical case.
So, when we measure the face of the quantum coin and see heads, can we say that it was heads all along and we just learnt it? What if we’d chosen to measure the colour and seen gold? In that case, we’d be saying, ah I’ve seen gold so it must have been gold all along. In the classical case, that works. But in the quantum case, it can’t have a definite colour and face at the same time. So it appears that we are not simply learning properties of the quantum state.