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Aspects of Holography And Quantum Error Correction

  • Author(s): Rath, Pratik;
  • Advisor(s): Nomura, Yasunori;
  • et al.
Abstract

The holographic principle has been a central theme in most of the progress in the field of quantum gravity in recent years. Our understanding of the AdS/CFT duality, the best known embodiment of the holographic principle, has taken a quantum leap in the last decade. A key role in the elucidation of how the holographic duality functions has been played by ideas from quantum information theory. In particular, the modern understanding of the holographic dictionary is that it works as a quantum error correcting code.

In this dissertation, we focus on a two-pronged approach to developing a deeper insight into the framework of quantum gravity. Firstly, despite the fact that we have learnt a lot about quantum gravity from AdS/CFT, it is not directly applicable to our universe which is an accelerating cosmological spacetime. Taking inspiration from the holographic principle and formulating ideas from AdS/CFT in the abstract language of quantum error correction, we take some preliminary steps in freeing ourselves from the crutches of AdS spacetimes and understanding features of holography in a wider class of spacetimes. We develop a framework for holography in general spacetimes using the Ryu-Takayanagi formula as a postulate and discuss conditions for bulk reconstruction, the existence of a bulk dual and qualitative features of putative holographic theories in arbitrary spacetimes.

Secondly, the holographic dictionary is not completely understood even within the realm of AdS/CFT. We clarify some aspects and propose novel entries to the AdS/CFT dictionary which shed light on how a gravitational description of a quantum mechanical system emerges holographically. In particular, this includes an understanding of how the holographic computation of Renyi entropy arises from a general feature of quantum error correction, supplemented by the special property that gravitational states have maximally mixed edge modes. Further, we resolve a long standing conjecture about the nature of tripartite entanglement of holographic states. Finally, we propose novel holographic duals to the reflected entropy in the presence of entanglement islands, and the Connes cocycle flow.

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