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arXiv:1901.03335 · Physical Review A

Collisional unfolding of quantum Darwinism

Steve Campbell, Barış Çakmak, Özgür Esat Müstecaplıoğlu, Mauro Paternostro, Bassano Vacchini

Published Apr 3, 2019• 41 citations
arXivHTMLPDF

Abstract

We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e., where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ``ancillas.'' By exploiting versatility of this framework, we show that one can transition from a ``Darwinistic'' to an ``encoding'' environment by simply tuning their interaction. Furthermore, we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, thus showing that system decoherence alone is not sufficient. Finally, we demonstrate that the observation of quantum Darwinism is sensitive to a nonuniform system-environment interaction.

DOI
10.1103/physreva.99.042103

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An explanation for the quantum-to-classical transition has long been sought after since the haydays of the field. Decoherence theory and open quantum system dynamics have paved the way, showing how a system can become correlated with, and so lose information into the environment. Quantum Darwinism, and its more stringent cousins Strong Quantum Darwinism and Spectrum Broadcast Structures, seek to explain how this information loss is achieved in such a way as to be objective, classical and redundant. However there remains questions as to how the structure of the environment, states and types of interactions can give rise to this redundant encoding. In this thesis, we collect the work of 3 of our papers, exploring these questions. First, we show how information from one environment can spread to another. Then we show how commutativity can play a role in the emergence of objectivity. Lastly, we move beyond a single, pure system to a more realistic bipartite one, with both classical and quantum correlations between the subsystems. We shall show how interactions between only these subsystems can mediate the redundancy of others, and how these can lower bound and upper bound other forms of interactions between said subsystems and the environment.
Quantum system interacting with environment can induce redundant encoding of the information of system into a multipartite environment, which is the essence of quantum Darwinism. At the same time, environment may scramble the initially localized information about the system. We mainly investigate the relevance between information scrambling in environment and the emergence of quantum Darwinism. First, we generally identify that when the system shows a Darwinistic behavior system information that is initially localized in the environment is not scrambled, while when Darwinism disappears scrambling occurs.We then verify our result through a collision model where the system, consisting of one or two qubits, interacts with an ensemble of environmental ancillas.Moreover, dependent on the nature of system-environment interactions, our results also shows that the single qubit and two-qubit systems behave differently for the emergence of QD and the scrambling, but the above relevance between them remains valid.
The authors study the quantum-to-classical transition from the perspective of a new exactly solvable collisional model that can induce the same dynamics on a qubit regardless of the level of entanglement with its environment. This property reveals a mechanism for decoherence without system-environment entanglement. The paper also assess the role of entanglement in quantum Darwinism analytically in this setting, and conclude that it only takes place in the presence of quantum correlations between system and environment.
The authors study the quantum-to-classical transition from the perspective of a new exactly solvable collisional model that can induce the same dynamics on a qubit regardless of the level of entanglement with its environment. This property reveals a mechanism for decoherence without system-environment entanglement. The paper also assess the role of entanglement in quantum Darwinism analytically in this setting, and conclude that it only takes place in the presence of quantum correlations between system and environment.
A quantum system interacting with a multipartite environment can induce redundant encoding of the information of a system into the environment, which is the essence of quantum Darwinism. At the same time, the environment may scramble the initially localized information about the system. Based on a collision model, we mainly investigate the relationship between information scrambling in an environment and the emergence of quantum Darwinism. Our results show that when the mutual information between the system and environmental fragment is a linear increasing function of the fragment size, the tripartite mutual information (TMI) is zero, which can be proved generally beyond the collision model; when the system exhibits Darwinistic behavior, the TMI is positive (i.e., scrambling does not occur); when we see the behavior of an "encoding" environment, the TMI is negative (i.e., scrambling occurs). Additionally, we give a physical explanation for the above results by considering two simple but illustrative examples. Moreover, depending on the nature of system and environment interactions, it is also shown that the single qubit and two-qubit systems behave differently for the emergence of quantum Darwinism, and hence the scrambling, while their relationship is consistent with the above conclusion.
Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent noninteracting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification in the manner of quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multimode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.