This is the approach we have taken in this book, because it is the simplest way to learn how to do calculations in quantum mechanics.
However, any physical theory should really tell us what is going on at the microscopic level. Just cataloguing the probabilities of events does not give a satisfactory explanation of how nature behaves.
To achieve this, we need to introduce States of Reality. There are broadly three different ways in which this can be implemented.
Quantum states are short-hand for the preparation procedure, and nothing more
Quantum states are a complete description of reality
The orthodox interpretation of the quantum state is that it gives a complete description of the system. So the quantum states are themselves the (only) states of reality.
This means we have a fundamental indeterminism in the outcomes of measurements.
Also, the quantum state collapse when we make a measurement is a mysterious non-unitary process.
The quantum state may be incomplete, and there are hidden variables that must be added to the description of the system. The measurement outcomes are now deterministic, since each outcome originates from a unique state of reality.
However, what are these hidden variables, and why can't we see them? What properties do they have?
Quantum states are supplemented with hidden variables to form states of reality
ψ-epistemic of the second kind
The quantum state may be just an expression of our lack of knowledge about the quantum system, and there are other states of reality that determine the measurement outcomes.
The "mysterious" collapse of the quantum state upon measurement is then simply a consequence of our updated knowledge of the system.
Quantum states represent our knowledge of the states of reality