Abstract
Quantum steering is a kind of quantum feature between quantum entanglement and Bell non-locality. Due to its special asymmetry, quantum steering plays an important role in many aspects of quantum information processing and thus has been widely concerned. There are many contributions on quantum steering in bipartite systems up to now, while tripartite systems have more complex structures than bipartite systems and then have more diversified steering scenarios. In this paper, two types of quantum steering scenarios are introduced for a tripartite quantum system, named “one-sided device-independent steering and “two-sided device-independent steering. Each of them contains two levels according to the separability of the local hidden states and the independence of the local hidden variables, respectively. Based on giving the mathematical definitions of these steering scenarios, some necessary and sufficient conditions for a state to be unsteerable are obtained and sufficient conditions for a state to be steerable are also established.
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