  An implementation of quantum absorption chillers with three qubits has been
recently proposed, that is ideally able to reach the Carnot performance regime.
Here we study the working efficiency of such self-contained refrigerators,
adopting a consistent treatment of dissipation effects. We demonstrate that the
coefficient of performance at maximum cooling power is upper bounded by 3/4 of
the Carnot performance. The result is independent of the details of the system
and the equilibrium temperatures of the external baths. We provide design
prescriptions that saturate the bound in the limit of a large difference
between the operating temperatures. Our study suggests that delocalized
dissipation, which must be taken into account for a proper modelling of the
machine-baths interaction, is a fundamental source of irreversibility which
prevents the refrigerator from approaching the Carnot performance arbitrarily
closely in practice. The potential role of quantum correlations in the
operation of these machines is also investigated.
