Entanglement Robustness in Trace Decreasing Quantum Dynamics

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