Dynamics of multipartite quantum steering for different types of decoherence channels

Multipartite quantum steering, a unique resource for asymmetric quantum network information tasks, is very fragile to the inevitable decoherence, which makes it useless for practical purposes. It is thus of importance to understand how it decays in the presence of noise channels. We study the dynamic behaviors of genuine tripartite steering, reduced bipartite steering, and collective steering of a generalized three-qubit W state when only one qubit interacts independently with the amplitude damping channel (ADC), phase damping channel (PDC) or depolarizing channel (DC). Our results provide the region of decoherence strength and state parameters that each type of steering can survive. The results show that these steering correlations decay the slowest in PDC and some non-maximally entangled states more robust than the maximally entangled ones. Unlike entanglement and Bell nonlocality, the thresholds of decoherence strength that reduced bipartite steering and collective steering can survive depend on the steering direction. In addition, we find that not only one party can be steered by a group system, but also two parties can be steered by a single system. There is a trade-off between the monogamy relation involving one steered party and two steered parties. Our work provides comprehensive information about the effect of decoherence on multipartite quantum steering, which will help to realize quantum information processing tasks in the presence of noise environments.