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Paper IPM / Physic / 12769  


Abstract:  
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 3tangle, and the entropy of the 8charge 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 D3branes whose wrapping around the six compact dimensions T^6 provides the stringtheoretic interpretation of the charges and we associate the threequbit basis vectors,  ABC> (A,B,C=0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N=8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan's E_7 supset [SL(2)]^7 invariant. The qubits are naturally described by the seven vertices ABCDEFG of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that E_7 has a natural structure of an Ograded algebra. This in turn provides a novel imaginary octonionic interpretation of the 56=7 x 8 charges of N=8: the 24=3 x 8 NSNS charges correspond to the three imaginary quaternions and the 32=4 x 8 RR to the four complementary imaginary octonions. N=8 black holes (or black strings) in five dimensions are also related to the bipartite entanglement of three qutrits (3state systems), where the analogous measure is Cartan's E_6 supset [SL(3)]^3 invariant.
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