Three-qubit interpretation of BPS and non-BPS $STU$ black holes

Following the recent trend we develop further the black hole analogy between quantum information theory and the theory of extremal stringy black hole solutions. We show that the three-qubit interpretation of supersymmetric black hole solutions in the $STU$ model can be extended also to include nonsupersymmetric ones. First we show that the black hole potential can be expressed as one half the norm of a suitably chosen three-qubit entangled state containing the quantized charges and the moduli. The extremization of the black hole potential in terms of this entangled state amounts to either suppressing bit flip errors (BPS case) or allowing very special types of flips transforming the states between different classes of non-BPS solutions. We are illustrating our results for the example of the $D2–D6$ system. In this case the bit flip errors are corresponding to sign flip errors of the charges originating from the number of $D2$ branes. After moduli stabilization the states depending entirely on the charges are maximally entangled graph states (of the triangle graph) well known from quantum information theory. An $N=8$ interpretation of the $STU$ model in terms of a mixed state with fermionic purifications is also given.