The Darwinian nature of Wojciech Zurek's theory of Quantum Darwinism is evaluated against the criteria of a Darwinian process as understood within Universal Darwinism. The characteristics of a Darwinian process are developed including the consequences of accumulated adaptations resulting in adaptive systems operating in accordance with Friston's free energy principle and employing environmental simulations. Quantum theory, as developed in Zurek's research program and encapsulated by his theory of Quantum Darwinism is discussed from the view that Zurek's derivation of the measurement axioms implies that the evolution of a quantum system entangled with environmental entities is determined solely by the nature of the entangled system. There need be no further logical foundation. Quantum Darwinism is found to conform to the Darwinian paradigm in unexpected detail and is thus may be considered a theory within the framework of Universal Darwinism. With the inclusion of Quantum Darwinism within Universal Darwinism and the explanatory power of Darwinian processes extended beyond biology and the social sciences to include the creation and evolution of scientific subject matter within particle physics, atomic physics and chemistry, it is suggested that Universal Darwinism may be considered a candidate 'Theory of Everything' as anticipated by David Deutsch.
In this thesis, I present my work during my Ph.D. in quantum Darwinism. It is a original project, which has been peer-reviewed and accepted for publication in a respected international journal. In the first chapters, I recalled the essential concepts to understand quantum Darwinism, and in the two last, I present my works. The quantum Darwinism concept was constructed to explain a possible quantum-to-classical transition. My main interests are to find the quantum Darwinism implications in the system’s dynamics and to find more realistic models where it applies. The first work was finished and published while the second is still in progress. In the first model I studied quantum Darwinism in a many-body system of quantum harmonic oscillators where the subenvironments neither interact nor correlate between themselves. Through analytical and numerical calculations, we observed quantum Darwinism from two different approaches. We show quantum Darwinism through the BPH approach in a model for the first time. In contrast with a recently published work, we also show that quantum Darwinism can be observed even in a system with a high degree of non-Markovianity, and proposed a more suitable way to quantify it. In the second work, we investigate quantum Darwinism in a more realistic model where the subenvironments can become strongly correlated. The model consists of a two-level atom interacting with a fermionic environment and was used to study orthogonality catastrophe. As both orthogonality catastrophe and quantum Darwinism comes with decoherence, we are investigating if these two concepts are correlated. Beyond that, we chose this model because it can be mapped in a bosonic model of the Tonks-Girardeau gas enabling an experimental implementation with cold atoms. We are performing numerical and analytical calculations in this work. In the sixth chapter, I present the first result and describe what is missing.
Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an
N-level environment via a random matrix coupling. We propose a partial trace method to suitably and consistently partition the effective
N-level environment and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that quantum Darwinism can apparently emerge under the Perez trace even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism and the nature of information and spectrum broadcast structure.