ar X iv : h ep - t h / 06 02 06 1 v 1 7 F eb 2 00 6 Strings , Black Holes , and Quantum Information

We find multiple relations between extremal black holes in string theory and 2-and 3-qubit systems in quantum information theory. We show that the entropy of the axion-dilaton extremal black hole is related to the concurrence of a 2-qubit state, whereas the entropy of the STU black holes, BPS as well as non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit states with the string theory states with some number of D-branes. We identify a set of " large " black holes with the maximally entangled GHZ-class of states and some " small " black holes with bipartite or W states. We sort out the relation between 3-qubit states, twistors, octonions, and black holes. We give a simple expression for the entropy and the area of stretched horizon of " small " black holes in terms of 2-tangles of a 3-qubit system. Finally, we show that the most general expression for the black hole and black ring entropy in N=8 supergravity/M-theory, which is given by the famous quartic Cartan E 7(7) invariant, can be reduced, using the SU(8) symmetry, to Cayley's hyperdeterminant describing the 3-tangle of a 3-qubit state.