A Study of Measurement Using Open Quantum Systems

Open quantum systems are quantum systems that are exposed to the environment. As a consequence, these systems do not obey the Schrödinger equation; and this gives rise to a phenomenon known as decoherence. My Thesis Proposal will be on using the formalism of open quantum systems to shed light on some foundational questions of quantum theory, specifically, the measurement problem. I model the measuring apparatus as an external environment, characterized by a set of Lindblad operators, acting on a quantum system of interest through via the Lindblad equation. I derive the general solution for the Lindblad equation with a general two level Hamiltonian and one Hermitian Lindblad operator. I then investigate which conditions the Lindblad operator and the Hamiltonian must satisfy in order to represent a measurement. This analytical solution could be useful in describing real-life experiments described by two-level systems, and it sets the stage for a more general calculation using a non-Hermitian Lindblad operator.