  Thermal attenuator channels model the decoherence of quantum systems
interacting with a thermal bath, e.g., a two-level system subject to thermal
noise and an electromagnetic signal travelling through a fiber or in
free-space. Hence determining the quantum capacity of these channels is an
outstanding open problem for quantum computation and communication. Here we
derive several upper bounds on the quantum capacity of qubit and bosonic
thermal attenuators. We introduce an extended version of such channels which is
degradable and hence has a single-letter quantum capacity, bounding that of the
original thermal attenuators. Another bound for bosonic attenuators is given by
the bottleneck inequality applied to a particular channel decomposition. With
respect to previously known bounds we report better results in a broad range of
attenuation and noise: we can now approximate the quantum capacity up to a
negligible uncertainty for most practical applications, e.g., for low thermal
noise.
