Abstract
As a direct consequence of the interplay between the superposition principle of quantum mechanics and the dynamics of open systems, decoherence is a recurring theme in both foundational and experimental exploration of the quantum realm. Decoherence is intimately related to information leakage of open systems and is usually formulated in the setup of “system + environment” as information acquisition of the environment (observer) from the system. As such, it has been mainly characterized via correlations (e.g., quantum mutual information, discord, and entanglement). Decoherence combined with redundant proliferation of the system information to multiple fragments of environment yields the scenario of quantum Darwinism, which is now a widely recognized framework for addressing the quantum-to-classical transition: the emergence of the apparent classical reality from the enigmatic quantum substrate. Despite the half-century development of the notion of decoherence, there are still many aspects awaiting investigations. In this work, we introduce two quantifiers of classicality via the Jordan product and uncertainty, respectively, and then employ them to quantify decoherence from an information-theoretic perspective. As a comparison, we also study the influence of the system on the environment.
Highlights
A fundamental hallmark of quantum mechanics is the superposition principle [1,2], which leads naturally to coherence and interference [3]
In this work, motivated by previous studies, and following quantitative investigations of coherence and superposition [73,74,75,76,77,78,79,80,81,82,83,84], we aimed at quantifying decoherence induced by the environment, which may be helpful for quantitatively characterizing certain features of the quantum-to-classical transition and quantum Darwinism
When we focus on the system and ignore the environment, the dynamics of a state ρ of a d-dimensional quantum system is mathematically described by a quantum channel in the Kraus representation form [11,87]
Summary
A fundamental hallmark of quantum mechanics is the superposition principle [1,2], which leads naturally to coherence and interference [3]. Decoherence usually refers to the decay of the off-diagonal entries of the system density matrix (in the basis of the pointer observable) caused by evolution of the combined “system + environment” It is characterized as the establishing of correlations between the system and the environment, which causes the system to behave in a classical manner. In this work, motivated by previous studies, and following quantitative investigations of coherence and superposition [73,74,75,76,77,78,79,80,81,82,83,84], we aimed at quantifying decoherence induced by the environment, which may be helpful for quantitatively characterizing certain features of the quantum-to-classical transition and quantum Darwinism. We consider only finite dimensional systems, it seems that many results can be readily extended to infinite dimensional cases
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