Abstract
In this work, we study quantum decoherence as reflected by the dynamics of a system that accounts for the interaction between matter and a given field. The process is described by an important information geometry tool: Fisher’s information measure (FIM). We find that it appropriately describes this concept, detecting salient details of the quantum–classical changeover (qcc). A good description of the qcc report can thus be obtained; in particular, a clear insight into the role that the uncertainty principle (UP) plays in the pertinent proceedings is presented. Plotting FIM versus a system’s motion invariant related to the UP, one can also visualize how anti-decoherence takes place, as opposed to the decoherence process studied in dozens of papers. In Fisher terms, the qcc can be seen as an order (quantum)–disorder (classical, including chaos) transition.
Highlights
The essential quantum decoherence concept arose in the early 1980s due to, among others, Zeh, Zurek, and Habib [1,2,3]
In Fisher terms, the quantum–classical changeover can be seen as an order–disorder transition
Our conclusions refer to the probability distribution that describes the classical– quantum transition in our model
Summary
The essential quantum decoherence concept arose in the early 1980s due to, among others, Zeh, Zurek, and Habib [1,2,3]. The emergence of the classical world in which we live from its quantum substratum has become a compelling issue that attracts much exciting work and intense, enlightening discussion We revisit it here from the viewpoint of information geometry and one of its central subjects: Fisher information. Information geometry is the study of statistical models (families of probability distributions) from a Riemannian geometric perspective. In this framework, a statistical model plays the role of a manifold. If our system lies in a rather ordered state, represented by a narrow probability distribution function (PDF), we face a Shannon entropy of S ∼ 0 and a FIM of F ∼ Fmax. In a very disordered state, one can consider an almost flat PDF and F ∼ 0 [13]
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