Irreversibility and symmetry principles in quantum information
Author(s)
Cirstoiu, Cristina
Type
Thesis
Abstract
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the
concept of quantum operations. If there is an
underlying symmetry principle, additional structures emerge.
The central question we address is, What are the consequences of global or local gauge symmetry
on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation.
Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.
concept of quantum operations. If there is an
underlying symmetry principle, additional structures emerge.
The central question we address is, What are the consequences of global or local gauge symmetry
on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation.
Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.
Version
Open Access
Date Issued
2018-12
Date Awarded
2019-07
Copyright Statement
Creative Commons Attribution NonCommercial Licence
Advisor
Jennings, David
Rudolph, Terry
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)