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Title: The role of supersymmetry in the black hole/qubit correspondence
Author: Dahanayake, Duminda
ISNI:       0000 0004 2693 8603
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2010
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This thesis explores the numerous relationships between the entropy of black hole solutions in supergravity and the entanglement of multipartite systems in quantum information theory: the so-called black hole/qubit correspondence. We examine how, through the correspondence, the dyonic charges in the entropy of supersymmetric black hole solutions are directly matched to the state vector coefficients in the entanglement measures of their quantum information analogues. Moreover the Uduality invariance of the black hole entropy translates to the stochastic local operations and classical communication (SLOCC) invariance of the entanglement measures. Several examples are discussed, with the correspondence broadening when the supersymmetric classification of black holes is shown to match the entanglement classification of the qubit/qutrit analogues. On the microscopic front, we study the interpretation of D-brane wrapping configurations as real qubits/qutrits, including the matching of generating solutions on black hole and qubit sides. Tentative generalisations to other dimensions and qubit systems are considered. This is almost eclipsed by more recent developments linking the nilpotent U-duality orbit classi cation of black holes to the nilpotent classi cation of complex qubits. We provide preliminary results on the corresponding covariant classi cation. We explore the interesting parallel development of supersymmetric generalisations of qubits and entanglement, complete with two- and three-superqubit entanglement measures. Lastly, we briefly mention the supergravity technology of cubic Jordan algebras and Freudenthal triple systems (FTS), which are used to: 1) Relate FTS ranks to threequbit entanglement and compute SLOCC orbits. 2) Define new black hole dualities distinct from U-duality and related by a 4D/5D lift. 3) Clarify the state of knowledge of integral U-duality orbits in maximally extended supergravity in four, five, and six dimensions.
Supervisor: Duff, Michael Sponsor: Dorothy Hodgkin Postgraduate Award
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral