Negativity of quantumness and non-Markovianity in a qubit coupled to a   thermal Ising spin bath system
  We propose a scheme to characterize the non-Markovian dynamics and quantify the non-Markovianity via the non-classicality measured by the negativity of quantumness. By considering a qubit in contact with a critical Ising spin bath and introducing an ancilla, we show that revivals of negativity of quantumness indicate the non-Markovian dynamics. Furthermore, a normalized measure of non-Markovianity based on the negativity of quantumness is introduced and the influences of bath criticality, bath temperature and bath size on the non-Markovianity are discussed. It is shown that, at the critical point, the decay of non-Markovianity versus the size of spin bath is fastest and the non-Markovianity is exactly zero only in the thermodynamic limit. Besides, non-trivial behaviours of negativity of quantumness such as sudden change, double sudden changes and keeping constant are found for different relations between parameters of the initial state. Finally, how the non-classicality of the system is affected by a series of bang-bang pulses is also examined. 
Zheng-Da Hu, Yixin Zhang, and Ye-Qi Zhang
quant-ph