Unitarity of black hole evaporation in final-state projection models

Sujoy K. Modak, Daniel Sudarsky

Karera Reksa

Seth Lloyd, John Preskill

Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.

Ali Akil, Lorenzo Giannelli, Leonardo Modesto +3 more

Black hole evaporation is one of the most striking phenomena at the interface between gravity and quantum physics. In Hawking's semi-classical treatment, where matter is quantum mechanical and the spacetime is definite and classical, evaporation leads to an apparent loss of unitarity of the overall evolution, and to the so-called black hole information paradox. Here, we go beyond this semi-classical treatment and formulate a toy quantum model of black hole evaporation that allows the black hole to evolve into a superposition of being fully evaporated and not fully evaporated, consistent with the Hawking particles being in a coherent superposition of different energy levels. We model Hawking particle production by the repeated action of quantum-controlled unitaries, generating emission from the quantum black hole and accounting for a quantum coherent back-reaction on the black hole matter state. We show that the probability of full annihilation of the black hole matter increases with time until the black hole is, asymptotically, fully evaporated in every branch of the quantum superposition. We prove that under natural assumptions, this evaporation model is unitary, such that the initial state can in principle be recovered from the final asymptotic state of the radiation.

Sujoy K. Modak, Leonardo Ortíz, Igor Peña +1 more

Ran Li, Jin Wang

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.