James Owen Weatherall in Nautilus:
Physicists know how to use quantum theory—your phone and computer give plenty of evidence of that. But knowing how to use it is a far cry from fully understanding the world the theory describes—or even what the various mathematical devices scientists use in the theory are supposed to mean. One such mathematical object, whose status physicists have long debated, is known as the quantum state.
One of the most striking features of quantum theory is that its predictions are, under virtually all circumstances, probabilistic. If you set up an experiment in a laboratory, and then you use quantum theory to predict the outcomes of various measurements you might perform, the best the theory can offer is probabilities—say, a 50 percent chance that you’ll get one outcome, and a 50 percent chance that you’ll get a different one. The role the quantum state plays in the theory is to determine, or at least encode, these probabilities. If you know the quantum state, then you can compute the probability of getting any possible outcome to any possible experiment.
But does the quantum state ultimately represent some objective aspect of reality, or is it a way of characterizing something about us, namely, something about what some person knows about reality? This question stretches back to the earliest history of quantum theory, but has recently become an active topic again, inspiring a slew of new theoretical results and even some experimental tests.