Decoherence, Anti-Decoherence, and Fisher Information

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.

Keywords: Fisher information; information geometry; semiclassical descriptions.

Figure 1

Anti-decoherence process. Fisher information $\mathcal{F}$ vs. I for an ample range that encompasses all three classical, semi-classical, and quantum regions.

Figure 2

Decoherence process. Fisher information $\mathcal{F}$ vs. $1/I$ for an ample rater range that encompasses the three classical, semi-classical, and quantum regions. Classicity is seen on the right with a relatively high FIM value.

Figure 3

Details of the transitional semi-quantum zone are observable in this plot. In Fisher terms, the quantum–classical changeover can be seen as an order (quantum)–disorder (classical, including chaos) transition.