Entanglement dynamics of two independent qubits in environments with and without memory

TL;DR

This paper presents a method to analyze the entanglement evolution of two independent qubits in environments with or without memory, highlighting how initial state purity, entanglement, and non-Markovian effects influence entanglement dynamics.

Contribution

It introduces a general procedure for modeling the dynamics of multiple qudits in arbitrary environments and applies it to study non-Markovian effects on two-qubit entanglement.

Findings

Entanglement decay depends on initial state purity and entanglement degree.

Non-Markovian environments can slow down entanglement loss.

Temperature influences entanglement dynamics in Markovian environments.

Abstract

A procedure to obtain the dynamics of $N$ independent qudits ($d$-level systems) each interacting with its own reservoir, for any arbitrary initial state, is presented. This is then applied to study the dynamics of the entanglement of two qubits, initially in an extended Werner-like mixed state with each of them in a zero temperature non-Markovian environment. The dependence of the entanglement dynamics on the purity and degree of entanglement of the initial states and on the amount of non-Markovianity is also given. This extends the previous work about non-Markovian effects on the two-qubit entanglement dynamics for initial Bell-like states [B. Bellomo \textit{et al.}, Phys. Rev. Lett. \textbf{99}, 160502 (2007)]. The effect of temperature on the two-qubit entanglement dynamics in a Markovian environment is finally obtained.