Holographic spacetime, black holes and quantum error correcting codes: a review

Abstract

This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

Correlation functions of the Bjorken flow in the holographic Schwinger-Keldysh approach

“…This is especially important in context of superfluid fluctuations since quantum dynamics is important at coherence time and length scales which are shorter than the scattering time and the mean free path respectively (see [14] for an excellent related discussion)-non-linearities can potentially cause novel non-trivial effects such as quantum corrections to the long time tails. 27 More generally, we would like use the horizon cap method to study holographic (evaporating) black holes interacting with heat baths or dynamical reservoirs, and understand the reconstruction of the islands [51,57] (which include the black hole interior) from Hawking quanta. In such cases, semi-holographic formulations for open quantum systems (see [58,59] and also [60] for instance) can provide useful models.…”

“…See[50,51] for recent reviews on current progress in resolving black hole information paradoxes with substantial discussion on the role played by hair degrees of freedom at the horizon.…”

Quantum Error Correction: Noise-Adapted Techniques and Applications

“…We will conclude with a quick survey of some recent results in this area and refer to [29] for a detailed review of this emerging field. The first concrete proposal for an approximate recovery map that could solve the problem of bulk reconstruction involved a variant of the Petz map, often called the twirled Petz map [77].…”

“…Next we survey some interesting applications of noise-adapted recovery maps, especially in the context of many-body quantum systems. We also briefly touch upon the interesting role that approximate recovery maps are coming to play in the AdS/CFT setting [29].…”

Entropy of Radiation with Dynamical Gravity

“…The whole surface is the union of the island surface and its partner on the thermofield double side. These have been previously studied in , and reviewed in [92][93][94][95][96][97] It is clear that whenever these island surfaces exist and depending on their relative area to the HM surface, we can either have constant for all times or initially rising Page curves. However, when such surfaces don't exist this story breaks and we lose any hope of describing evolution as unitary.…”