Joint momenta-coordinates states as pointer states in quantum decoherence

TL;DR

This work rigorously proves that joint momenta-coordinates states saturating generalized uncertainty are the genuine pointer states in a damped harmonic oscillator modeled by a Lindblad master equation. The analysis demonstrates that such states remain pure and robust only in the underdamped regime with $\Omega^{2}=\omega^{2}-\mu^{2}>0$, deriving explicit diffusion coefficients $D_{xx}, D_{pp}, D_{px}$ and corresponding phase-space variances that keep the generalized uncertainty equal to the minimum $\frac{\hbar^{2}}{4}$. The authors connect decoherence theory with quantum phase-space formalism by showing these states saturate the predictability sieve, thus minimizing entropy production. In the overdamped case, no pure time-invariant pointer states exist, clarifying the physical distinction between dynamical regimes. Overall, the results extend pointer-state identification beyond Gaussian approximations and reinforce a phase-space perspective on classical robustness within quantum dynamics with potential applications in error-resistant quantum information.

Abstract

Quantum decoherence provides a framework to study the emergence of classicality from quantum systems by showing how interactions with the environment suppress interferences and select robust states known as pointer states. Earlier studies have linked Gaussian coherent states to pointer states. More recently, it was conjectured that more general quantum states called joint momenta-coordinates states may serve as more suitable candidates to be pointer states. These states are associated to the concept of quantum phase space and saturate, by definition, generalized uncertainty relations. In this work, we rigorously prove this conjecture. Building on the Lindblad framework for the damped harmonic oscillator, and applying Zurek's predictability-sieve criterion, we analyze both underdamped and overdamped regimes. We show that only in the underdamped case do joint momenta-coordinates states remain pure and robust for all times, establishing them as the true pointer states. This extends Isar's earlier underdamped treatment, generalizes the concept beyond Gaussian approximations, and embeds classical robustness in the quantum phase space formalism, with potential applications in error-resistant quantum information.

Theorems & Definitions (6)

• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof