Perturbation theory under the truncated Wigner approximation reveals how system-environment entanglement formation drives quantum decoherence

TL;DR

This paper introduces a theoretical framework combining the truncated Wigner approximation with perturbation theory to analyze how system-environment entanglement drives quantum decoherence, with implications for preserving quantum coherence.

Contribution

It develops a scalable, flexible method to study system-environment entanglement and decoherence, demonstrated on the spin-boson model, revealing strategies to mitigate decoherence.

Findings

Entanglement formation correlates with decoherence at zero temperature.

Suppression of low-frequency environmental modes reduces decoherence.

The framework provides analytical insights into perturbative contributions.

Abstract

Quantum decoherence is the disappearance of simple phase relations within a discrete quantum system as a result of interactions with an environment. For many applications, the question is not necessarily how to avoid (inevitable) system-environment interactions, but rather how to design environments that optimally preserve a system's phase relations in spite of such interactions. The formation of system-environment entanglement is a major driving mechanism for decoherence, and a detailed understanding of this process could inform strategies for conserving coherence optimally. This requires scalable, flexible, and systematically improvable quantum dynamical methods that retain detailed information about the entanglement properties of the environment, yet very few current methods offer this combination of features. Here, we address this need by introducing a theoretical framework wherein we combine the truncated Wigner approximation with standard time-dependent perturbation theory allowing for computing expectation values of operators in the combined system-environment Hilbert space. We demonstrate the utility of this framework by applying it to the spin-boson model, representative of qubits and simple donor-acceptor systems. For this model, our framework provides an analytical description of perturbative contributions to expectation values. We monitor how quantum decoherence at zero temperature is accompanied by entanglement formation with individual environmental degrees of freedom. Based on this entanglement behavior, we find that the selective suppression of low-frequency environmental modes is particularly effective for mitigating quantum decoherence.