Strings, Black Holes, and Quantum Information

Abstract

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 "small" black holes with separable, bipartite and 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 a norm and 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 to Cayley's hyperdeterminant describing the 3-tangle of a 3-qubit state.

31 pages, 10 figures. A version to appear in Physical Review

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• Hidden symmetries of the Nambu-Goto action
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• Topics in Cubic Special Geometry
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• A finite geometric toy model of space-time as an error correcting code
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