• Markovian noise
• quantum entanglement
• quantum entanglement survival time
• quantum information theory

Entanglement represents a powerful, yet fragile resource that can be easily degraded by an external environment. There exist methods to determine the entanglement survival time (EST) that work properly when one has a correct characterization of noise, and one might also wonder what happens when there is no complete noise characterization. In this thesis, we attempt to address this problem using a statistical approach. More specifically, our purpose is to obtain results that do not concern a specific noise model but an entire ensemble of possible noises. Clearly, in this type of analysis, it is important to define the type of ensemble to consider. In our study we have chosen to assume a distribution as unbiased as possible using methods from Random Matrix Theory. The only structure we added concerns the consideration of different weight parameters between the Hamiltonian and the dissipative component of noise.

We obtained the EST distributions in the simple, yet non-trivial case of two maximally entangled qubits under the action of a (local) Markovian noise. We analyzed such distributions with the purpose of obtaining a theoretical fit probability distribution function, we studied the relationship between their characteristic times and the chosen parameters, and we investigated the possible presence of correlations between the ESTs and the eigenvalues of the superoperator associated with the dynamical evolution of the system. Moreover, since from the study of the EST distributions emerged the presence of a limit distribution when the Hamiltonian component of the noise becomes predominant, we derived the theoretical expression of the superoperator that, properly sampled, allows one to obtain the limit distribution found with the numerical simulation.