On the fidelity of information retrieval in the black hole final state model with scrambling interactions

We study the fidelity of information retrieval in the black hole final state model by taking into account the interactions between the collapsing matter and the infalling Hawking radiation inside the event horizon. By utilizing a scrambling unitary operator to model these interactions, our direct calculations suggest that the information is almost lost during the process of black hole evaporation. We then proceed to employ the Yoshida-Kitaev decoding strategy for information retrieval. Although we observe a finite improvement in decoding fidelity, it does not reach unity. This indicates that the issue of unitarity in black hole evaporation may not be fully resolved within the framework of the final state model.