Decoherence, einselection, and the quantum origins of the classical

TLDR

Decoherence, caused by environmental interaction, destroys interference between pointer states, and in the macroscopic limit the combination of einselection with dynamics yields classical phase‑space structure as idealized points and trajectories. The paper investigates how environment‑induced superselection (einselection) selectively loses information. Einselection, together with system dynamics, projects the quantum Hilbert space onto classical points and trajectories in the macroscopic limit. Einselected pointer states remain stable, preserve correlations with the rest of the Universe, suppress non‑local Schrödinger‑cat states, and replace quantum entanglement with classical correlations during measurements.

Abstract

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.