Quantum Complexity and Chaos in Young Black Holes

We argue the problem of calculating retention time scales in young black holes is a problem of relative state complexity. In particular, we suggest that Alice's ability to estimate the time scale for a perturbed black hole to release the extra $n$ qubits comes down to her decoding the Hilbert space of the Hawking radiation. We then demonstrate the decoding task Alice faces is very difficult, and in order to calculate the relative state complexity she would either need to act with an exponentially complex unitary operator or apply an extremely fine-tuned future precursor operator to the perturbed state in $SU(2^{K})$.