We present the evidence for and intriguing black hole/qubit correspondence. This correspondence will map the entanglement classification of three and four qubits over to the BPS and extremal classification of black holes in the STU model. We will start by looking at BPS black holes and use a variety of means to classify them and calculate their orbits. We will discover that three qubits, or more accurately, three real qubits will exhibit exactly the same structure as the black holes. This will allow us to identify the entropy of the black hole with the entanglement of the qubits. A mathematical framework known as the Freudenthal triple system will be used to classify both systems. We will be able to use the wrapped branes picture of the black holes as an explanation of the binary nature of the qubit. We will then develop this correspondence further and use the mathematics of nilpotent orbits and the Kostant-Sekiguchi correspondence to directly map the classification of extremal black holes to the entanglement classification of four qubits. We will discover that the classification of four qubits is related to the distinct orbits that exists of the SL(2,C)4 on nilpotent (2, 2, 2, 2). We will also discover that the extremal black holes of the STU model correspond to nilpotent orbits of the Lie algebra so4,4. We will then use the Kostant-Sekiguchi correspondence as a diffeomorphism between these two types of orbits.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:555899 |
| Date | January 2012 |
| Creators | Rubens, William |
| Contributors | Duff, Michael |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/9594 |
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