Black Holes, Qubits and Octonions

Understand

We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory.

• The first example is provided by the measure of the tripartite entanglement of three qubits, known as the 3-tangle, and the entropy of the 8-charge STU black hole of N=2 supergravity, both of which are given by the [SL(2)]^3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845.
• There are further relationships between the attractor mechanism and local distillation protocols.
• At the microscopic level, the black holes are described by intersecting D3-branes whose wrapping around the six compact dimensions T^6 provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, |ABC> (A,B,C=0 or 1), with the corresponding 8 wrapping cycles.