  The non-isometric holographic model of the black hole interior stands out as
a potential resolution of the long-standing black hole information puzzle since
it remedies the friction between the effective calculation and the microscopic
description. In this study, combining the final-state projection model, the
non-isometric model of black hole interior and Hayden-Preskill thought
experiment, we investigate the information recovery from decoding Hawking
radiation and demonstrate the emergence of the Page time in this setup. We
incorporate the effective modes into the scrambling inside the horizon, which
are usually disregarded in Hayden-Preskill protocols, and show that the Page
time can be identified as the transition of information transmission channels
from the EPR projection to the local projections. This offers a new perspective
on the Page time. We compute the decoupling condition under which retrieving
information is feasible and show that this model computes the black hole
entropy consistent with the quantum extremal surface calculation. Assuming the
full knowledge of the dynamics of the black hole interior, we show how
Yoshida-Kitaev decoding strategy can be employed in the modified
Hayden-Preskill protocol. Furthermore, we perform experimental tests of both
probabilistic and Grover's search decoding strategies on the 7-qubit IBM
quantum processors to validate our analytical findings and confirm the
feasibility of retrieving information in the non-isometric model. This study
would stimulate more interests to explore black hole information problem on the
quantum processors.
