I will talk about transport properties of a charge qubit embedded between two Luttinger liquids. This is realized, e.g., by a double-antidot system placed between the edge states of the integer $\nu=1$ or fractional $\nu=1/3$ quantum Hall systems. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin which realizes an orbital Kondo impurity embedded in a Luttinger liquid, while the inter-antidot tunnelling acts like an impurity magnetic field. The latter tends to destabilize the Kondo fixed point at $\nu=1/3$ and produce an effective inter-edge scattering, as in quasiparticle tunnelling in quantum point contacts. We relate the inter-edge backscattered conductance to the spin relaxation of the Kondo impurity and calculate it in various limits for both $\nu=1$ and $\nu=1/3$.