Leonid Pastur

Dynamics of Qubits in Random Matrix Environment

We consider a model of the evolution of one and two qubits, embedded in an environ- ment. Unlike the well-known spin-boson model, which often used to model translation- invariant and macroscopic environments, we model the environment with large random matrices that widely used to describe multiconnected disordered media of mesoscopic and even nanoscopic sizes. An important property model is that it can describe the non-Markovian evolution, allowing for the backflow of energy and information from the environment into qubits. We obtain an asymptotically exact expression for the reduced density matrix of qubits valid for all typical realizations of a disordered environment. Using then de- tailed analytical and numerical analysis of the expression, we find several interesting patterns of the qubit evolution, including the disappearance of entanglement at cer- tain moments and especially its subsequent reappearance. These patterns are known in quantum information science as sudden death and sudden birth of entanglement. They were found earlier in special particular solutions and approximations of the spin- boson models. Our results obtained for non-macroscopic and disordered environment demonstrates the robustness and universality of patterns. Combined with some quan- tum information science procedures (e.g. mix-up distillation), the results can lead to significant slower decay of entanglement up to its asymptotic conservation.