Noise tolerance of recycled entanglement detection by sequential and independent observers

Entanglement, as a fundamental resource for quantum information processing, can be witnessed cyclically by arbitrary many sequential and independent observers or pairs of observers without regard to the influence from noisy devices. However, from a practical perspective, imperfections of devices can result in the decay or even destroy of quantum entanglement in the aforementioned scenario. In the paper, we analyze the persistency of entanglement witnessing by sequential and independent observers in the noisy single-side or both-side scenario, where noises arise from errors in entanglement generation, transmission, and imperfection in measurements. We first devote to finding the noisy persistency conditions, under which there still exist arbitrary many pairs of observers can witness entanglement. Then, we obtain the noisy persistency conditions in the single-side sequential sharing scenario. Excluding these cases of the aforesaid persistency conditions, the maximal number of pairs of observers which can witness entanglement may be constrained to be finite because of the influence of noises. Therefore, finally, we discover the change pattern of the maximal number of pairs of observers with more general noises.