Quantum dynamics with classical noise

Huang, Qin (2020) Quantum dynamics with classical noise. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this thesis, we study the evolution of qubits evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. For a single qubit exposed to such noise, we show that the noise-averaged qubit density matrix converges to a specific final state, in the limit of large time t. We find that the convergence speed is polynomial in 1=t, with a power that depends on the regularity and the low frequency behaviour of the noise probability density. We evaluate the final state explicitly in the regimes of weak and strong off-diagonal noise. We show that the process implements the well-known dephasing channel in the localized and delocalized basis, respectively. Furthermore, we consider the evolution of the entanglement of two (or more) qubits subject to Gaussian noises with varying means and variances. We consider two different cases: individual noise where each qubit feels an independent noise, and common noise where all qubits are subjected to the same noise. We find the following characteristics of entanglement, measured by the concurrence of qubits. Initially entangled states lose their amount of entanglement in time due to the presence of the noise. The decay of entanglement happens more quickly for common noise than for individual noise. We also detect creation of entanglement due to the common noise: for some initially disentangled states, entanglement is created for intermediate times and then decays to zero in the long time again.

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