Executive Summary : | The study aims to investigate the dynamics of quantum spin chains, specifically the propagation of locally coded information through the spin chain to distant spins. It also explores how quantum correlations redistribute during closed-system evolution, which can lead to decoherence. This is particularly important in open-system evolution, where a quantum system interacts with a quantum measuring apparatus or a noisy environment. The study will focus on the distribution of quantum correlations when quantum operations act on spins at two different locations, either in a correlated or uncorrelated manner. The effects of quantum noise introduced through these operations will depend on whether it arises from a coherent process or an incoherent process. Coherent correlated noise introduces new correlations and anti-correlations that may be out of phase with the background distribution of quantum correlations. Incoherent correlated noise introduces decoherence effects that may adversely affect the propagation of correlations through the quantum spin chain. The study will study both magnon-number conserving and non-conserving dynamics, including Heisenberg dynamics and transverse field XY models. The redistribution of quantum correlation in the presence of correlated quantum noise will be investigated numerically. The scrambling of information can be sensitive to the background dynamics' integrability or non-integrability. The Loschmidt Echo, a measure of the revival probability of a quantum state under imperfect time reversals, can also capture these effects. The study will also examine the effect of quantum noise on momentum distribution and Loschmidt echo. |