  We present two particular decoding procedures for reconstructing a quantum
state from the Hawking radiation in the Hayden-Preskill thought experiment. We
work in an idealized setting and represent the black hole and its entangled
partner by $n$ EPR pairs. The first procedure teleports the state thrown into
the black hole to an outside observer by post-selecting on the condition that a
sufficient number of EPR pairs remain undisturbed. The probability of this
favorable event scales as $1/d_{A}^2$, where $d_A$ is the Hilbert space
dimension for the input state. The second procedure is deterministic and
combines the previous idea with Grover's search. The decoding complexity is
$\mathcal{O}(d_{A}\mathcal{C})$ where $\mathcal{C}$ is the size of the quantum
circuit implementing the unitary evolution operator $U$ of the black hole. As
with the original (non-constructive) decoding scheme, our algorithms utilize
scrambling, where the decay of out-of-time-order correlators (OTOCs) guarantees
faithful state recovery.
