Quantitative analysis reveals memory effects in a quantum system utilizing the Jaynes–Cummings model and trace distance measurements, suggesting dependence on history.
We quantitatively investigate the physical origins of the non-Markovianity measure proposed in our previous work, which can be directly interpreted as memory effects, i.e., the dependence of a quantum system’s future evolution on its history. Using the properties of the trace norm and the trace distance, we find that the strength of memory effects in an evolution is upper (lower) bounded by the sum (difference) of two quantities. One originates from (bounded by) the change of environment state caused by the system, the other from (bounded by) the correlations between the system and the environment. The simulation results for the Jaynes–Cummings model show that the two origins may contribute to the memory effects in different manners, depending on the initial states of the environment and the system.
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Hou et al. (2025) studied this question.
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