Spectrum Broadcast Structures for Discrete and Continuous Variables in Open Quantum Systems

Abstract

We develop tools apt for the quantitative study of the dynamical emergence of Spectral Broadcast Structures (SBS) due to environmental monitoring. In the past, efforts have been made to bound the proximity of an arbitrary state undergoing non-unitary evolution to the nearest SBS state (in the trace distance sense). This dissertation presents the first of such bounds which has been substantiated as well as provides sufficient conditions under which a broad family of multipartite states converge to SBS states asymptotically in time. We also develop an SBS theory for continuous variables (SBSCV); i.e. the dynamics will now be generated by self-adjoint operators with purely continuous spectrum. We create a theory for SBSCV that parallels that of SBS and develop tools for its quantitative study.