Aspects of Holographic Entanglement Measures

Kulkarni, Harshal (2023) Aspects of Holographic Entanglement Measures. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Harshal Kulkarni (18MS056)) Thesis_18MS056.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

Entanglement measures, in particular the entanglement entropy, have undoubtedly played a very crucial role in quantum information and quantum computing. However, since the decade-old advancement linking the entanglement entropy to geometric quantities via AdS/CFT, considerable progress has happened at this intersection of quantum gravity and quantum information, allowing us to deepen our understanding of quantum gravity by using purely information-theoretic techniques. This has led to concretely study and make progress toward the program of emergence of spacetime from entanglement and information, an idea speculated long back by Wheeler. Majority of the understanding so far has been limited to the entanglement entropy, which is a bi-partite entanglement measure. However, to gain additional insights into characterizing states in holographic CFTs and going beyond the already interesting ideas like bulk reconstruction, studying multi-partite entanglement and respective measures is essential. Even purely from the point of view of quantum information, a study of multi-partite entanglement is interesting in its own right to store and transfer information using entanglement. In the first half of this project, we perform a detailed study of various aspects and implications of the entanglement entropy and holography and its implications for understanding the emergence of geometry and gravitation from entanglement. The latter half is concerned with studying aspects of multi-partite entanglement measures, in particular the one with holographic duals, which we call the multi-entropy. We conjecture and find convincing evidence for inequalities of monotonicity of multi-entropy under coarse-graining, which takes us closer to establishing the multi-entropy as a good measure of multi-partite entanglement.

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