Is superposition a real quantum state or just an unknown

Question

Take the Schrodinger's cat thought experiment, without peeking inside the box the state of the cat is unknown but we know of 2 outcomes which are either alive or dead. Once we decided to peek inside we will know which one of the 2 possible outcomes it is, so I suspect superposition in this case is due to our ignorance. But the doubleslit clearly demonstrates superposition although we can't see it in action. The quantum eraser is even bizarre as it is like we open the box in a complete darkness, so I am wondering if superposition is even a quantum state such as the cat is actually both alive and dead at the same time and the action of opening the box to peek inside changes the fate of the cat in that instant forever.

Answer 1

Is superposition a real quantum state or just an unknown ?

Theories that posit that quantum superposition is a byproduct of our ignorance of (possibly inaccessible) attributes with deterministic values are called hidden variable theories.

Various experimental validations of Bell's theorem and related results have almost certainly ruled out local hidden variable theories i.e. hidden variable theories in which causal influence is limited by the speed of light (I say "almost certainly" because there may be some minor technical loopholes that are not yet entirely closed). The only hidden variable theories that are consistent with experimental results therefore seem to be those that allow causal influences and communication to take place faster than the speed of light (and possibly instantaneously).

Answer 2

A (pure) state is a state: there is nothing unknown about it.

The best possible example to clarify this is polarized light. Suppose you have light with diagonal polarization: $\vert \nearrow\rangle$. A polarizer with this orientation will let 100% of the light described by $\vert\nearrow\rangle$ go through, and a polarizer with orientation $\nwarrow$ will allow 0% of the light to go through, so there is nothing unknown about that state.

If however you choose to make measurements using horizontal or vertical polarizers, then you state $\vert \nearrow\rangle$ will sometimes go through and sometimes not. The probabilities are tied to the choice of measurement, now to the description of the state (at least for pure states).

Of course if $\vert\updownarrow\rangle$ and $\vert\leftrightarrow\rangle$ denote the states “alive” and “dead”, there is no analogous description to $\vert\nearrow\rangle$, i.e. there is no apparatus that can measure something in between alive and dead, but that’s strength and the weakness of the cat paradox: you are restricted to measurements in a specific basis so you should not be too surprised to find results that have a difficult interpretation given such limitation. Likewise, some results make a lot more intuitive sense using polar or spherical coordinates rather than Cartesian, so don’t be surprised if you struggled if you are restricted to a single choice of coordinate system.