Unique entanglement time evolution of two-qubit product separable and extended Werner-like states in a discrete qubit environment

TL;DR

This paper explores how different environmental conditions affect the entanglement dynamics of two-qubit states, revealing unique evolution patterns and the influence of noise and system interactions on entanglement revival and dissipation.

Contribution

It provides a detailed analysis of entanglement evolution in various noisy environments, highlighting the disjoint evolution subspaces of PS and EWL states and the inverse relationship between environment and subsystem interactions.

Findings

Complete entanglement revivals in pure homogeneous environments.

Attenuation of concurrence with increasing number of environments.

Entanglement dissipation depends on interaction strength distribution.

Abstract

This study investigates the parameters affecting the entanglement time evolution of product separable (PS) and extended Werner-like (EWL) states in homogeneous, white noise, and mixed environments. In a pure homogeneous environment, both states demonstrate complete entanglement revivals, where an increase in the number of environments leads to an attenuation of concurrence. The PS state exhibits gaps and never reaches a maximum entanglement, whereas maximum purity EWL states (Bell states) maintain or periodically reach maximum entanglement. Hence, the PS and EWL states have a disjoint entanglement time evolution subspaces. Interestingly, the environment interaction and subsystem coupling interaction that influence entanglement have an inverse time relationship under a constant value of concurrence. Placing the system of interest in a white noise environment induces entanglement dissipation, with the dissipation time dependent on the width of random distribution of interaction strengths rather than the magnitude of interaction strength. In a distinct qubit environment, the entanglement time evolution of the PS state depends on the distribution of the number of environments. Moreover, combining homogeneous and white noise environments results in entanglement dynamics that exhibit characteristics of both homogeneous and white noise.