A three-qubit interpretation of BPS and non-BPS STU black holes

TL;DR

This paper extends the three-qubit quantum information interpretation of extremal black holes in the STU model to include non-supersymmetric solutions, linking black hole properties to quantum entanglement and error correction.

Contribution

It demonstrates that both BPS and non-BPS black hole solutions can be described using three-qubit entangled states, connecting charge configurations and moduli stabilization to quantum error types.

Findings

Black hole potential expressed as three-qubit state norm

Extremization corresponds to suppressing or transforming bit flip errors

Maximally entangled graph states represent stabilized charge configurations

Abstract

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 non-supersymmetric 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 supressing 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.