  Losses in quantum communication lines severely affect the rates of reliable
information transmission and are usually considered to be state-independent.
However, the loss probability does depend on the system state in general, with
the polarization dependent losses being a prominent example. Here we analyze
biased trace decreasing quantum operations that assign different loss
probabilities to states and introduce the concept of a generalized erasure
channel. We find lower and upper bounds for the classical and quantum
capacities of the generalized erasure channel as well as characterize its
degradability and antidegradability. We reveal superadditivity of coherent
information in the case of the polarization dependent losses, with the
difference between the two-letter quantum capacity and the single-letter
quantum capacity exceeding $7.197 \cdot 10^{-3}$ bit per qubit sent, the
greatest value among qubit-input channels reported so far.
