QUANTITATIVE CORRELATIONS EXTENDED FROM EXTERNAL ENVIRONMENT AND STOCASTIC EVOLUTION

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In this thesis work, we have engaged in quantum systems that are composed in situations where typically quantum correlations are induced by the external environment and observation.
Quantum correlations play a primary role in quantum information and in quantum computation. In the last decade, much research has been devoted to studying and understanding how two quantum systems can be related to each other. 
The type of correlation we want to go to study takes the name of entanglement that we could translate with non separable interlacing, entanglement and a sort of quantum correlation.
This phenomenon of entanglement and of paramount importance in quantum mechanics also for the repercussions that the full understanding of this phenomenon might have on quantum information. L’interest in the subject and also very strong from a mathematical point of view-as modeling for the study of continuous time problems are involved stochastic differential equations (EDS), change of probability, deterministic evolution equations (master equations). After the introduction of this concept, it is important to introduce a quantity to measures it. There are various possible measures proposed in the literature, but we choose to use concurrence as it is perhaps the simplest to deal with from a mathematical point of view. The concurrence and a quantum analogue of the classical correlation index: concurrence nothing Waterman separable state, without any entanglement