[Paper Review] Entanglement Wedge Reconstruction and the Information Paradox

Geoffrey Penington|arXiv (Cornell University)|May 20, 2019

Black Holes and Theoretical Physics90 references44 citations

TL;DR

The paper uses entanglement wedge reconstruction and quantum RT surfaces to derive the Page curve and Hayden-Preskill decoding in evaporating black holes, showing interior information gradually escapes via non-perturbative effects and state-dependent reconstructions.

ABSTRACT

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $β/2π\log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

Motivation & Objective

• Motivate resolving the black hole information paradox within AdS/CFT using entanglement wedge reconstruction.
• Demonstrate a Page-time phase transition of the quantum extremal surface from inside to outside the horizon.
• Show how the Page curve and Hayden-Preskill decoding emerge from holographic entanglement structure.
• Explain state dependence of interior reconstructions and minimal state dependence to avoidFirewalls.

Proposed method

• Adopt absorbing boundary conditions and an auxiliary radiation reservoir to model black hole evaporation.
• Use quantum extremal surfaces and the generalized entropy A/4G_N + S_bulk to define entanglement wedges.
• Identify a non-empty quantum extremal surface inside the horizon that becomes the RT surface at the Page time.
• Derive the entanglement entropy S as S = min(S_rad, A_hor/4G_N) via the quantum extremal surface transition.
• Generalize Hayden-Preskill to large diaries and mixed initial states within the entanglement wedge framework.
• Discuss state dependence through approximate operator algebra quantum error correction and minimal state dependence bounds.

Experimental results

Research questions

• RQ1 How does the entanglement wedge reconstruction change during evaporative black hole evolution?
• RQ2 Can the Page curve and Hayden-Preskill decoding criterion be derived from holographic entanglement and RT surfaces in an evaporating black hole?
• RQ3 What role do non-perturbative corrections play in interior reconstruction and information escape?
• RQ4 How does state dependence affect interior reconstructions for different initial black hole microstates?
• RQ5 Under what conditions can interior information be reconstructed with minimal state dependence before evaporation begins?

Key findings

• A phase transition at the Page time where the non-empty quantum extremal surface becomes the RT surface, yielding the Page curve.
• The entanglement entropy S between the CFT and the radiation reservoir is S = min(S_rad, A_hor/4G_N) to leading order.
• Interior information partially encoded in early Hawking radiation, avoiding a firewall without abandoning semiclassical bulk physics.
• Hayden-Preskill decoding criteria emerge from entanglement wedge reconstruction, including generalizations to large diaries and unknown initial states.
• State dependence of interior reconstructions arises but can be constrained; minimal state dependence suffices to avoid AMPSS firewall paradox.
• Before evaporation, a state-independent interior reconstruction exists for code spaces with entropy less than the Bekenstein-Hawking entropy; this suffices to avoid typical-state firewalls.