Optimal Manipulation Of Correlations And Temperature In Quantum Thermodynamics

TL;DR

This thesis explores optimal strategies for cooling and creating correlations in quantum thermodynamics, deriving bounds based on environmental parameters and analyzing the limits of correlation creation at various temperatures.

Contribution

It introduces a simple, attainable bound for quantum cooling based on a single environmental parameter and provides new insights into the limits of correlation creation at different temperatures.

Findings

Derived a universal bound for quantum cooling based on environment parameters.

Solved the correlation creation problem for finite-dimensional systems at zero temperature.

Proposed a conjecture for the attainability of bounds in all dimensions.

Abstract

This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined. The connection that these paradigms have with other existing refrigeration techniques such as heat bath algorithmic cooling (HBAC), the resource theoretic approach to quantum thermodynamics, and autonomous cooling is then made. Each paradigm is then investigated on its own. This in particular allows for the derivation of a general and attainable bound. The bound is striking in its simplicity: it depends on a single parameter of the environment/machine used to cool the system of interest. The creation of correlations part is devoted to the quantitative study of how much correlations can be created for a given amount of energy. After having precisely formulated the problem of interest, we solve it for arbitrary finite dimensional bipartite systems for vanishing background temperatures. For non-vanishing background temperature the symmetry of the problem breaks down, making it much harder to tackle. When both systems are copies of each other, enough symmetry is restored to formulate an upper bound valid for all (finite) dimensional systems and prove its attainability for dimension 3 and 4. We furthermore conjecture, as well as show evidence for, the bound to be attainable in any dimension.