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arXiv:2304.12222 · Physical Review A

Complementarity between decoherence and information retrieval from the environment

Tae-Hun Lee, Jarosław K. Korbicz

Published Mar 22, 2024• 4 citations
arXivHTMLPDF

Abstract

We address the problem of the 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 recoilless 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 the 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 nontrivial 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.

DOI
10.1103/physreva.109.032221

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We address the problem of the 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 recoilless 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 the 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 nontrivial 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.
In this work, we investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.
The dynamics of an open quantum system in the high-temperature regime of the Caldeira-Leggett model using a Bohmian language is investigated. By expressing the density matrix in polar form, generalized continuity and Hamilton-Jacobi equations are obtained. Thermal effects appear explicitly in the former, while they influence the latter only indirectly through an effective potential. Remarkably, the effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions. Instead, it retains a nontrivial structure leading to a residual temperature dependence in the resulting dynamics. As a consequence, the resulting temperature-dependent-classical trajectories remain deterministic even in the presence of a thermal environment. This behavior contrasts with the stochastic dynamics observed in the Langevin description and reflects the ensemble-based nature of the present approach. To further explore the quantum-to-classical transition, a scaled version of the Caldeira-Leggett equation is introduced by scaling both the density matrix and Planck constant through a quantumness parameter. This parameter takes the value one in the fully quantum regime and smoothly approaches zero in the classical limit. Applications to Gaussian states demonstrate a gradual suppression of coherence and interference, governed jointly by thermal effects and the transition parameter.
This work presents a general model for open quantum systems using an information game along the lines of Jaynes' original work. It is shown how an energy based reweighting of propagators provides a novel moment generating function at each time point in the process. Derivatives of the generating function give moments of the time derivatives of observables. Aside from the mathematically helpful properties, the ansatz reproduces key physics of stochastic quantum processes. At high temperature, the average density matrix follows the Caldeira-Leggett equation. Its associated Langevin equation clearly demonstrates the emergence of dissipation and decoherence time scales, as well as an additional diffusion due to quantum confinement. A consistent interpretation of these results is that decoherence and wavefunction collapse during measurement are directly related to the degree of environmental noise, and thus occur because of subjective uncertainty of an observer.
The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicioğlu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schrödinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.
Understanding the behavior of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process of decoherence and the so-called quantum measurement problem. There have been many approaches to explore Markovian and non-Markovian dynamics within the framework of open quantum systems, but the richness of the ensuing dynamics is still not fully understood. In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on expanding the dynamics of the reduced system at high temperature in inverse powers of the high-frequency cutoff of the Ohmic spectral density of the environment and derive a non-Markovian master equation for the reduced density matrix for the case of a general potential. We also obtain a fully analytical solution in the free particle case. While the short-time behavior of this solution does not diverge substantially from the Markovian behavior, at intermediate times we find a resurgence of coherence, which we name lateral coherence. We identify this with a corresponding transient negative entropy production rate, which is understood to be characteristic of non-Markovian dynamics. We also analyze the positivity of the reduced density matrix and derive the corresponding Fokker-Planck equation in the classical limit.
We propose an effective field-theoretic framework for open quantum systems in which decoherence dynamics are influenced by an auxiliary scalar field acting as an informational memory degree of freedom. This additional field induces intrinsically non-Markovian behavior, leading to structured noise spectra and deviations from standard exponential decay. The resulting reduced dynamics are governed by a non-local memory kernel, capturing temporal correlations beyond conventional approaches. We show that the model predicts oscillatory modulations in coherence decay and provides improved fits to simulated qubit data compared to both exponential and stretched-exponential models. The framework also reproduces nontrivial residual structures and spectral features that are not accounted for in standard decoherence theories. To test these predictions, we propose an experimental protocol using superconducting qubits, where systems initialized under identical environmental conditions but with different controlled histories exhibit distinguishable decoherence dynamics. This history dependence offers a potential experimental signature of the proposed mechanism. Overall, this work provides a phenomenological extension of decoherence theory and highlights the role of memory effects and informational degrees of freedom in open quantum systems, suggesting new directions for both theoretical and experimental investigation.