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Trace decreasing dynamical maps are as physical as trace preserving ones;however, they are much less studied. Here we overview how the quantum Sinkhorntheorem can be successfully applied to find a two-qubit entangled state whichhas the strongest robustness against local noises and losses of quantuminformation carriers. We solve a practically relevant problem of finding anoptimal initial encoding to distribute entangled polarized qubits thoughcommunication lines with polarization dependent losses and extra depolarizingnoise. The longest entanglement lifetime is shown to be attainable with a statethat is not maximally entangled.

Entanglement robustness in trace decreasing quantum dynamics caused by depolarization and polarization dependent losses