Bob only needs at least k qubits from the black hole's Hawking radiation to decode Alice's quantum state.
Using energy conservation and a toy model, it becomes clear that Hawking radiation corresponds to heavy modes classically.
The toy-model relies on a clear distinction between heavy and soft modes based on thermodynamics properties, energy, and charge.
[6] Using a system of two Dicke models, it was found that when data is thrown into a black hole the initial spin information can be read after it has been scrambled into the cavity.
[6] If decoding fidelity is a constant, the black hole will act similarly to a mirror and reflect back any information that falls into it almost immediately.
Additionally, the early radiation and the black hole are initially maximally entangled, but decoherence emerges over time.