We present the evidence for and intriguing black hole / qubit correspondence.
This correspondence will map the entanglement classification of three and
four qubits over to the BPS and extremal classification of black holes in the
STU model. We will start by looking at BPS black holes and use a variety
of means to classify them and calculate their orbits. We will discover that
three qubits, or more accurately, three real qubits will exhibit exactly the same
structure as the black holes. This will allow us to identify the entropy of the
black hole with the entanglement of the qubits. A mathematical framework
known as the Freudenthal triple system will be used to classify both systems.
We will be able to use the wrapped branes picture of the black holes as an
explanation of the binary nature of the qubit.
We will then develop this correspondence further and use the mathematics
of nilpotent orbits and the Kostant-Sekiguchi correspondence to directly map
the classification of extremal black holes to the entanglement classification of
four qubits. We will discover that the classification of four qubits is related to
the distinct orbits that exists of the SL(2,C)4 on nilpotent (2, 2, 2, 2). We will
also discover that the extremal black holes of the STU model correspond to
nilpotent orbits of the Lie algebra so4,4. We will then use the Kostant-Sekiguchi
correspondence as a diffeomorphism between these two types of orbits.