This is my license thesis' repository
The Maximum Entropy Principle is utilized to construct an assignment map that enables the derivation of a microscopic state consistent with a coarse description of a multi-qubit system. Specifically, the coarse description corresponds to the information obtained from an imperfect measuring device. When performing measurements, there exists a non-zero probability that the measurement is conducted on a different particle than the intended one. Furthermore, the device can only measure a subset of the system's degrees of freedom. Assuming knowledge of the microscopic evolution, various effective dynamics are examined using the maximum entropy assignment map. These effective dynamics represent observable changes in the coarse description of the system.
Some of the investigated dynamics exhibit nonlinearity and dependence on the initial effective state, which provides a fundamental mechanism for the emergence of nonlinear dynamics from quantum mechanics. For instance, the dynamics induced by local unitary evolutions lose the periodicity of the underlying dynamics but demonstrate convergence to unitary dynamics as the number of particles increases. In other cases, such as dephasing channels, depolarization channels, and stabilization channels, the effective dynamics retain the same nature as the underlying dynamics, thereby resembling a quantum channel.
Moreover, it is discovered that the dynamics are linear in the extreme scenario where the probability of error is zero. This linearity arises from the fact that the only nonlinear component of the dynamics, the assignment map, becomes linear. Numerical investigations are conducted on an Ising chain consisting of up to nine particles. Additionally, the findings derived from the maximum entropy assignment map are compared with those obtained using another type of assignment map called the average assignment map. The average assignment map assigns the average of all compatible pure microscopic states to an effective state.
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