Enhanced quantumness via non-Markovianity

In this paper we address the issue of the interplay between non-Markovianity and nonclassicality of a system. We consider the action of non-Markovian environments on a qubit in terms of two models, a classical noise model and a quantum microscopic collision model. For both models we use the violation of the Leggett-Garg inequality (LGI) as a criterion of quantumness, and use the conditional past-future (CPF) correlation to measure non-Markovianity. Besides for the collision model, we also use violation of the nondiscord generating and detecting (NDGD) dynamics to indicate the nonclassicality. And LGI, NDGD, and CPF are probed sequentially by three projective measurements of some observable. In this paper we do not use the assumption of the quantum regression theorem and especially for the collision model the measurement backaction on the environment is explicitly considered. We find that compared with the Markovian dynamics the LGI can be violated for a longer time interval, i.e., non-Markovianity can preserve the quantumness of the system. For the collision model we find that for a specific measurement process, although the non-Markovianity cannot be detected, the effect of non-Markovianity of the system dynamics on nonclassicality still exists, and for some specific measurement operator the violation of both LGI and NDGD will never occur for the Markovian dynamics while with the enhancement of non-Markovianity the quantumness can appear. We also find that the NDGD can be violated for a much wider parameter regime than the LGI.