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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