Extremal Black Holes as Qudits

Abstract

We extend the black hole/qudit correspondence by identifying five and six-dimensional 1/2-BPS black string and hole charge vectors in N=8 and N=2 magic supergravities with qubits and qutrits over composition algebras. In D=6, this is accomplished via Hopf fibrations, which map qubits over composition algebras to rank one elements of Jordan algebras of degree two. An analogous procedure maps qutrits over composition algebras to D=5 charge vectors, which are rank one elements of Jordan algebras of degree three. In both cases, the U-duality groups are interpreted as qudit SLOCC transformation groups. We provide explicit gates for such transformations and study their applications in toroidally compactified M-theory.

19 pages, 1 figure, references updated

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• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• Orbits in Non-Supersymmetric Magic Theories
• Klein and Conformal Superspaces, Split Algebras and Spinor Orbits
• U-Duality and the Leech Lattice