Attractors, Black Holes and Multiqubit Entanglement

Abstract

Recently a striking correspondence has been established between quantum information theory and black hole solutions in string theory. For the intriguing mathematical coincidences underlying this correspondence the term “Black Hole Analogy” has been coined. The basic correspondence of the analogy is the one between the entropy formula of certain stringy black hole solutions on one hand and entanglement measures for qubit and qutrit systems on the other. In these lecture notes we develop the basic concepts of multiqubit entanglement needed for a clear exposition of the Black Hole Analogy. We show that using this analogy we can rephrase some of the well-known results and awkward looking expressions of supergravity in a nice form by employing some multiqubit entangled states depending on the quantized charges and the moduli. It is shown that the attractor mechanism in this picture corresponds to a distillation procedure of highly entangled graph states at the black hole horizon. As a further insight we also find a very interesting connection between error correcting codes, designs and the classification of extremal BPS and non-BPS black hole solutions.