GAUSSIAN QUANTUM RESOURCE THEORY
Quantum resource theories are a powerful mathematical framework for studying manifold phenomena in quantum physics, ranging from entanglement theory to quantum thermodynamics. The framework captures resource properties of different physical quantities and, from that, enables their quantitative study. Although different kinds of resource theories have been developed separately, recently there were also some attempts to establish a unified framework for general (finite-dimensional) resource theories. However, there has not been much research into general resource theories in infinite dimensions.
Gaussian states are the most important tool to study infinite-dimensional continuous-variable quantum systems due to their practical importance and rich mathematical structure. As there is an increasing interest in the resource-theoretic approach in quantum optics, it would be useful if there is a general framework for Gaussian resource theories. We will investigate the general structure of Gaussian resource theories and provide a mathematical toolbox for studying information-processing tasks in Gaussian quantum information. We will then apply these tools to appropriate resource theoretical scenarios, especially in quantum thermodynamics, to find novel insights.