Bearing in mind that it's generally an error to try to summarise anything about quantum mechanics in a paragraph or two:
Actually, it's the equivalent of finding socks in the dark. If two photons are produced by an interaction of spin zero then the two photons will have spin up and spin down, although you can't know which is which without measuring one. .
I'm sorry,. but the way you write that makes it seem that they have spin up and spin down, and then you measure them to find out which is which. If that's indeed what you meant, I'm afraid that's fundamentally incorrect.
The whole point about the weirdness of quantum entanglement is that the quanta are NOT in a state where one is up and one is down prior to the measurement. Only when you make the measurement does this happen. Prior to the measurement, quantum mechanics says that they are both in a state that is BOTH up and down at the same time.
In other words, quanta are not like socks. We can be reasonably sure that socks' measurable properties are fixed before we actually look at them. Not so with quanta.
You can think of this in this way: when you make a measurement on one of the quanta, it flips a coin that tells it whether to be up or down. Its twin quantum is then bound to give the opposite result. But prior to the coin toss, neither quantum knows how it will respond to a measurement. The most that can be said is that whatever the result of measuring one, the other will give the opposite result.