If two observers look at the same quantum object, will they see the same thing? Let's say two observers, one at the North pole and one at the South pole, both observe the Moon. Will they see the same Moon, or a subtly different Moon?
Intuitively it feels like they should see a different Moon - this is because each individual Moon photon can only be detected by one of the two observers. However if this is the case, then why would astronomical radio interferometry work? After all, there's no reason to suppose the photons each observer detects would be similar/coherent enough to interfere with the photons detected by the other observer.
 A: I think @Allure is asking 1) if a single quantum object (whose state is indeterminate) can be measured separately and independently by two different observers, and 2) if so, then can they get different results.
The answer is basically "yes" to 1) and "no" 2). An entangled pair of particles is, for all practical purposes, a single quantum object.  Observer A can measure one of the pair, while Observer B measures the other of the pair.  By doing their measurements on the quantum object, the observers entangle themselves with the quantum object. The only way the two observers can know if they have gotten different results is by comparing results, which entangles the observers.  As a result, both observers are entangled with the quantum object so they will agree on its state.
A: If the astronomers can measure quantum-scale properties of the moon, they will definitely obtain different results at that scale.  That's not really because they measure "different photons," though, but because outcomes of measurements of a noisy quantum system with a vast number of component subsystems will have prohibitively small probabilities of repeating.
However, radio interferometry is classical, not quantum interferometry, so it works just fine because any quantum effects are statistically washed out.  After all, Michelson and Morley did their famous interference experiment with white light from a non-coherent source before quantum mechanics was even studied.
