Nope. They don't "have" their own state until one of them is measured. But they do have a correlated state which exists before measurement, which says they have

Nope. They don't "have" their own state until one of them is measured. But they do have a correlated state which exists before measurement, which says they have opposite/same states. The individual states arise only after measurement. I'm not a physicist, but wrote a Quantum Simulator.