{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/30949"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/30949","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"Complexity And Entanglement In Quantum Gravity","abstract":"We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface.","abstract_html":"We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface.","abstract_has_math":false,"creators":["Kar, Arjun"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Vijay Balasubramanian"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020","date_published":"2020","updated_at":"2026-07-24T03:47:28Z","subjects":[],"languages":["en"],"rights":["Arjun Kar"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/30949","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Vijay Balasubramanian"]},{"key":"dc:creator","label":"Author","values":["Kar, Arjun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-18T01:06:12.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-22T17:55:10Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2001-01-01T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2020"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Arjun Kar"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/30949"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Complexity And Entanglement In Quantum Gravity"]}]}],"canonical_facts":{"dc:contributor.advisor":["Vijay Balasubramanian"],"dc:creator":["Kar, Arjun"],"dc:date":["2023-05-18T01:06:12.000"],"dc:date.accessioned":["2023-05-22T17:55:10Z"],"dc:date.available":["2001-01-01T00:00:00Z"],"dc:date.issued":["2020"],"dc:description.abstract":["We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/30949"],"dc:language":["en"],"dc:rights":["Arjun Kar"],"dc:title":["Complexity And Entanglement In Quantum Gravity"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:47:28Z"}