Quantum information recovery from a black hole with a projective measurement

We studied the Hayden-Preskill thought experiment with the local projective measurement. Compared to the original model, the measurement is applied to the Hawking radiation that was emitted after throwing the quantum diary into the black hole. Within this setup, we explored the information recovery from the black hole utilizing the Yoshida-Kitaev probabilistic strategy and demonstrated a perfect decoding in the ideal case. Additionally, we analyzed the decoherence effects from the environment on the decoding protocol. It shows that errors represented by the depolarizing channel can reduce the decoding probability and fidelity, while errors represented by the dephasing channel do not affect the decoding protocol. Furthermore, we discussed various aspects of the current model, including its relation to the black hole final state proposal and the quantum simulations of the decoding protocols. Especially, employing the graphical representations, we provide an intuitive derivation of the equivalence between the Yoshida-Kitaev protocol and Petz recovery map.