  Trace decreasing dynamical maps are as physical as trace preserving ones;
however, they are much less studied. Here we overview how the quantum Sinkhorn
theorem can be successfully applied to find a two-qubit entangled state which
has the strongest robustness against local noises and losses of quantum
information carriers. We solve a practically relevant problem of finding an
optimal initial encoding to distribute entangled polarized qubits though
communication lines with polarization dependent losses and extra depolarizing
noise. The longest entanglement lifetime is shown to be attainable with a state
that is not maximally entangled.
