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Non-Markovianity by Quantum Loss

In the study of open quantum systems, information exchange between system and its surrounding environment plays an eminent and important role in analysing the dynamics of open quantum system. In this work, by making use of the quantum information theory and intrinsic properties such as \emph{entropy exchange}, \emph{coherent information} and using the notion of \emph{quantum loss} as a criterion of the amount of lost information, we will propose a new witness, based on information exchange, to detect non-Markovianity. Also a measure for determining the degree of non-Markovianity, will be introduced by using our witness. The characteristic of non-Markovianity is clarified by means of our witness, and we emphasize that this measure is constructed based on the loss of information or in other word the rate of \emph{quantum loss} in the environment. It is defined in term of reducing correlation between system and ancillary. Actually, our focus is on the information which be existed in the environment and it has been entered to the environment due to its interaction with the system. Remarkably, due to choosing the situation which the "system +ancillary" in maximal entangled pure state, optimization procedure does not need in calculation of our measure, such that the degree of non-Markovianity is computed analytically by straightforward calculations.