Einstein–Podolsky–Rosen steering is a peculiar quantum nonlocal correlation and has unique physical characteristics and a wide application prospect. Even more importantly, multipartite steerable states have more vital applications in the future quantum information field. Thus, in this work, we explored the dynamics characteristics of both genuine multipartite steering (GMS) and genuine multipartite entanglement (GME) and the relations of both under an open tripartite system. Specifically, the tripartite decoherence system may be modeled by the three parties of a tripartite state that undergo the noisy channels. The conditions for genuine entangled and steerable states can be acquired for the initial tripartite state. The results showed that decoherence noises can degrade the genuine multipartite entanglement and genuine multipartite steering and even induce its death. Explicitly, GME and GMS disappear with the increase in the decoherence strength under the phase damping channel. However, GME and GMS rapidly decay to death with the increase in the channel-noise factor and then come back to life soon after in the bit flip channel. Additionally, the results indicate that GMS is born of GME, but GME does not imply GMS, which means that the set of genuine multipartite steerable states is a strict subset of the set of genuine multipartite entangled states. These conclusions may be useful for discussing the relationship of quantum nonlocal correlations (GME and GMS) in the decoherence systems.

In this letter, we investigate quantum correlations (quantum discord, concurrence and Bell nonlocality) in an open system (amplitude damping channel) with the Unruh effect under a Schwarzschild space-time. In an amplitude damping (AD) channel, we can discover that the Hawking-Unruh effects and decoherence will influence these quantum correlations. However, quantum correlations always decrease with increasing the AD decoherence strength, irrespective of whether there are Hawking-Unruh effects. The results also indicate that the impact of the AD decoherence on quantum correlations is stronger than that of the Hawking-Unruh effects. Besides, we find that if concurrence is present, Bell nonlocality may disappear. This means that the Bell nonlocal states are a strict subset of the entangled states. Furthermore, the redistributions of quantum correlations are discussed in detail under a Schwarzschild space-time. The results show that the reduced physically accessible quantum correlations can be redistributed to the physically inaccessible regions.