If two identical emitters are coupled to a common reservoir, entanglement can be generated during the decay process. When using Bell's inequality to examine the non-locality, however, it is possible that the bound cannot be violated in some cases. Here, we propose to use the steering inequality to examine the non-locality induced by a common reservoir. Compared with the Bell inequality, we find that the steering inequality has a better tolerance for examining non-locality. In view of the dynamic nature of the entangling process, we also propose to observe the quantum coherent dynamics by using the Leggett-Garg inequalities. We also suggest a feasible scheme, which consists of two quantum dots coupled to nanowire surface plasmons, for possible experimental realization
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