Entanglement Robustness in Trace Decreasing Quantum Dynamics

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 through 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.Quanta 2021; 10: 15–21

Trace decreasing quantum dynamical maps: Divisibility and entanglement dynamics

Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that this approach leads to incorrect conclusions about the dynamics divisibility, namely, one can observe an increase in the trace distance or the system-ancilla entanglement although the trace decreasing dynamics is completely positive divisible. We propose solutions to that problem and introduce proper indicators of the information backflow and the indivisibility. We also review a recently introduced concept of the generalized erasure dynamics that includes more experimental data in the dynamics description. The ideas are illustrated by explicit physical examples of polarization dependent losses.Comment: 12 pages, 3 figures, based on a talk delivered at the 41st International Conference on Quantum Probability and Related Topic