A master equation has been constructed for a global system-bath interaction both in the absence as well as presence of non-Markovian noise. For the memoryless case, it has been exactly solved for a paradigmatic class of two qubit states in high and zero temperature thermal environment. For the non-Markovian model, it has been solved for zero temperature bath. The evolution of quantum coherence and entanglement has been observed in presence of the above mentioned interactions. We show that the global part of the system-bath interaction compensates for the decoherence, resulting in slow down of coherence and entanglement decay. For an appropriately defined limiting case, both coherence and entanglement show freezing behaviour for the high temperature bath. In case of zero temperature bath, the mentioned interaction not only stabilizes the non-classical correlations, but also enhances them for a finite period. For the memory dependent case, we have seen that the global interaction enhances the back-flow of information from environment to the system, as it enhances the regeneration of coherence and entanglement. Also we have studied the generation of Quantum Fisher information by the mentioned process. An intuitive measure of non-classicality based on non-commutativity of quantum states has been considered. Bounds on generated quantum Fisher information has been found in terms of quantumness and coherence. This gives us a novel understanding of Quantum Fisher information as a measure of non-classicality.
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