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## Monday, October 13, 2008

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Black Holes, Qubits and Octonions

In perhaps what is the most up-to-date paper on the quantum computation-extremal black hole-division algebra correspondence, Duff et al review all previous conjectures and suggest an alternative interpretation for which the black hole charges are identified with components of reduced density matrices. The density matrix formulation of quantum mechanics is discussed and compared to the Jordan algebraic quantum mechanics, showing the two approaches are essentially equivalent. The exceptional Jordan algebra forbids a traditional Hilbert space formulation, hence the corresponding D=5 and D=4 supergravities remain somewhat of a mystery.

In perhaps what is the most up-to-date paper on the quantum computation-extremal black hole-division algebra correspondence, Duff et al review all previous conjectures and suggest an alternative interpretation for which the black hole charges are identified with components of reduced density matrices. The density matrix formulation of quantum mechanics is discussed and compared to the Jordan algebraic quantum mechanics, showing the two approaches are essentially equivalent. The exceptional Jordan algebra forbids a traditional Hilbert space formulation, hence the corresponding D=5 and D=4 supergravities remain somewhat of a mystery.

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## 3 comments:

143 pages, yikes! I need more time to read these things....

Density matrix formulation. Maybe that's why I'm getting a lot of IP hits the last few days.

Kea: Yes, 143 pages indeed. However, all these pages get you up to speed without having to read 15 or so other papers.

Carl: I'm quite pleased to see the density matrix formulation prove to be more natural in the black hole/quantum computational correspondence. Recall that the context is supergravity/M-theory, which lends credence to the use of density matrices in ordinary (non-gravitational) QFT.

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