Creation of Two-Particle Entanglement in Open Macroscopic Quantum Systems

TL;DR

This paper investigates how two-particle entanglement is generated in open macroscopic quantum systems of multiple spins interacting with thermal environments, revealing that entanglement diminishes as the system size grows.

Contribution

It provides a numerical and analytical study of entanglement creation in many-qubit systems coupled to thermal baths, showing limitations in entanglement generation with increasing qubits.

Findings

Entanglement decreases as the number of qubits increases.

No entanglement can be generated in the limit of infinitely many qubits.

Collective thermal environments cannot produce two-qubit entanglement in large systems.

Abstract

We consider an open quantum system of N not directly interacting spins (qubits) in contact with both local and collective thermal environments. The qubit-environment interactions are energy conserving. We trace out the variables of the thermal environments and N-2 qubits to obtain the time-dependent reduced density matrix for two arbitrary qubits. We numerically simulate the reduced dynamics and the creation of entanglement (concurrence) as a function of the parameters of the thermal environments and the number of qubits, N. Our results demonstrate that the two-qubit entanglement generally decreases as N increases. We show analytically that in the limit N tending to infinity, no entanglement can be created. This indicates that collective thermal environments cannot create two-qubit entanglement when many qubits are located within a region of the size of the environment coherence length. We discuss possible applications of our approach to the development of a new quantum characterization of noisy environments.