Investigation Of The Measure Based On Entanglement In Quantum Non-Markovian Processes

Any quantum systems inevitably interact with their environments,therefore quantum systems are always open.Open quantum dynamics can be divided into Markovian and and non-Markovian processes.For the Markovian process,the energy and information of the system can only flow to the environment unidirectionally and diffuse quickly in the environment,theirs no longer react to the system,which leads to the nomemory irreversible process.On the contrary,nonMarkovian processes,will exhibit some memory effect,in which the information and energy that flow into the environment previously will partially flow back to the system,making the present state evolution of the system dependent on its history.In recent years,the non-Markovian process has become a hot issue in the research of open quantum processes.The definition and measurement of Markovian and non-Markovian processes are the basic problems of open quantum dynamics.At present people have put forward a variety of non-Markovianity measures,including the measure based on divisibility,the measure based on trace distance,the measure based on entanglement ect.However,these non-Markovianity measures are not completely unified,The main content of this paper is to study the relationship between the three measures mentioned above.Our basic results are dynamical divisiblity must lead to the monotonic decrease of entanglement,but the converse is not true in general.The relation between the measures based on entanglement and trace distance is sophisticated.the monotonic decrease of trace distance does not necessarily lead to the monotonic decrease of entanglement,and the monotonic decrease of entanglementalso does not necessarily lead to the monotonic decrease of trace distance.