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Oxford Quantum Talks Archive

Black holes, qubits and octonions

Leron Borsten, Imperial College London
Categories, Logic and Foundations of Physics V, August 2009, Imperial College London

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. The black hole/qubit correspondence extends, via the Fano plane, to the 56 charge N=8 black holes and the "tripartite entanglement of seven qubits". The Fano plane provides the multiplication table of the seven imaginary octonions, reflecting the fact that E_7 has a natural structure of an O-graded algebra. Turning to the microscopic picture of these black holes we may associate the qubits with the wrapping cycles of D3-branes in type IIB string theory. At present this correspondence remains at a purely mathematical level. However, further investigation, whether or not it eventually reveals a physical duality, will certainly provide insights into both sides of the QI/String equation. Recent examples include (1) A Freudenthal triple classification of three qubits and (2) Black holes admitting a Freudenthal dual (3) a new role for the octonions in M-theory.

[video] [streaming video]