chaos, extradimensions, black hole.

Introduction
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In a recent paper [@Viennot], we have studied the decoherence phenomenon induced on a qubit (supported by the spin of a fermion) falling into a black hole. This study has needed some strong semi-classical approximations in quantum field theory on curved space-time (only first quantization of the fermion, localization of the qubit (WKB approximation), adiabatic approximation of the dynamics). In the present paper, we want to consider this problem in a “quantum gravity context”. An interesting model of quantum black holes arises in the matrix model with D-branes [@Asplund; @Berenstein; @Aoki]. In the BFSS (Banks-Fischler-Shenker-Susskind) matrix theory [@BFSS], a stack of D0-branes forms a noncommutative D2-brane represented by Hermitian matrices (the noncommutative coordinates on the D2-brane). The initial conditions on these matrices fix the topology of the D2-brane (as for example a fuzzy sphere) and adding small initial fluctuations induces thermalization of the system in a state corresponding to a black hole horizon. By adding a fermionic string stretched from the D2-brane to a probe D0-brane, as for example in [@Berenstein], we have a qubit model supported by the spin inner degree of freedom of the fermionic string. It has been proved [@Asano; @Gur; 