Evolution of Entanglement of Two Qubits Interacting through Local and Collective Environments

TL;DR

This paper rigorously analyzes the dynamics of entanglement between two qubits interacting via local and collective environments using resonance perturbation theory, providing insights into decoherence, disentanglement, and relaxation times relevant for quantum technologies.

Contribution

It introduces a new approach based on resonance perturbation theory to analyze entanglement dynamics without finite time limitations, including a novel classification of decoherence times.

Findings

Derived expressions for decoherence, disentanglement, and relaxation times.

Identified conditions for creation and decay of entanglement.

Discussed applications in superconducting quantum computation.

Abstract

We analyze rigorously the dynamics of the entanglement between two qubits which interact only through collective and local environments. Our approach is based on the resonance perturbation theory which assumes a small interaction between the qubits and the environments. The main advantage of our approach is that the expressions for (i) characteristic time-scales, such as decoherence, disentanglement, and relaxation, and (ii) observables are not limited by finite times. We introduce a new classification of decoherence times based on clustering of the reduced density matrix elements. The characteristic dynamical properties such as creation and decay of entanglement are examined. We also discuss possible applications of our results for superconducting quantum computation and quantum measurement technologies.