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Complementarity between decoherence and information retrieval from the environment

Published 24 Apr 2023 in quant-ph | (2304.12222v2)

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.

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