The role of mutual information in the Page curve

Abstract

In this work, we give two proposals regarding the status of connectivity of entanglement wedges and the associated saturation of mutual information. The first proposal has been given for the scenario before the Page time depicting the fact that at a particular value of the observer's time $t_b=t_R$ (where $t_R\ll \beta$), the mutual information $I(R_{+}:R_{-})$ vanishes representing the disconnected phase of the radiation entanglement wedge. We argue that this time is the Hartman-Maldacena time at which the fine-grained entropy of radiation goes as $S(R)\sim \log (\beta )$, where $\beta$ is the inverse of Hawking temperature of the black hole. On the other hand, the second proposal probes the crucial role played by the mutual information of black hole subsystems in obtaining the correct Page curve of radiation.

v1: 7 pages LaTex, 2 figures, v2: 9 pages LaTex, 2 figures. Accepted for publication in Physical Review D

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• Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole
• Island of Reissner-Nordstr$\ddot{\mathbf{o}}$m anti-de Sitter black holes in the large $d$ limit
• Infrared Regularization and Finite Size Dynamics of Entanglement Entropy in Schwarzschild Black Hole
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime
• Effect of backreaction on Island, Page curve and Mutual Information
• Island of acoustic black hole in Schwarzschild spacetime
• Page curves and island's delays in asymptotically flat 2d spacetimes with injections
• Investigating the role of mutual information in the Page curve for a functional renormalization group improved Schwarzschild black hole
• New insights on mutual information in the island approach to the Page curve