Complementarity between decoherence and information retrieval from the environment

TL;DR

This paper explores the fundamental limits of information extraction from environments in open quantum systems, introducing new concepts like the distinguishability length and Quantum Fisher Information kernel to deepen understanding of decoherence and information dynamics.

Contribution

It provides a model-independent, hybrid quantum-classical solution for open quantum dynamics, revealing new lengthscales and kernels that enhance understanding of environmental information flow.

Findings

Discovery of the distinguishability length scale.

Introduction of the Quantum Fisher Information kernel.

Relations between disturbance and information gain in environment.

Abstract

We address the problem of fundamental limitations of information extraction from the environment in open quantum systems. We derive a model-independent, hybrid quantum-classical solution of open dynamics in the recoil-less limit, which includes environmental degrees of freedom. Specifying to the celebrated Caldeira-Leggett model of hot thermal environments, ubiquitous in everyday situations, we reveal the existence of a new lengthscale, called distinguishability length, different from the well-known thermal de Broglie wavelength that governs the decoherence. Interestingly, a new integral kernel, called Quantum Fisher Information kernel, appears in the analysis. It complements the well-known dissipation and noise kernels and satisfies disturbance-information gain type of relations, similar to the famous fluctuation-dissipation relation. Our results complement the existing treatments of the Caldeira-Legget model from a non-standard and highly non-trivial perspective of information dynamics in the environment. This leads to a full picture of how the open evolution looks like from both the system and the environment points of view, as well as sets limits on the precision of indirect observations.