“Information” in the quantum sense refers to the waveform of the quantum system as a whole, which is kind of a weird thing to get one’s head around.

Even in the case of chaotic pendulums, there’s no theoretical principle that keeps us from observing and accounting for every particle and quanta of energy involved and using that to prove that the waveform of the entire pendulum is consistent with itself and the expected evolution from previous states.

But the event horizons of black holes seem to break that rule, because the waveforms of black holes can be described with just three properties; mass, charge, and spin. There didn’t seem to be “room” for them to encode all the waveforms of anything that falls inside until Stephen Hawking theorized that it could be saved in polarization states of the event horizon boundary and black holes would gradually radiate it away.