Limitation of entanglement due to spatial qubit separation

TL;DR

This paper investigates how spatial separation affects entanglement robustness between two qubits coupled to a thermal bosonic environment, providing exact solutions and insights into decoherence-free subspaces.

Contribution

It offers an exact analytical solution for two spatially separated qubits' entanglement dynamics under pure dephasing, clarifying the influence of physical parameters.

Findings

Entanglement robustness depends on temperature, coupling strength, and separation.

Identifies regimes where robust and fragile entanglement descriptions fail.

Provides explicit conditions for decoherence-free subspace stability.

Abstract

We consider spatially separated qubits coupled to a thermal bosonic field that causes pure dephasing. Our focus is on the entanglement of two Bell states which for vanishing separation are known as robust and fragile entangled states. The reduced two-qubit dynamics is solved exactly and explicitly. Our results allow us to gain information about the robustness of two-qubit decoherence-free subspaces with respect to physical parameters such as temperature, qubit-bath coupling strength and spatial separation of the qubits. Moreover, we clarify the relation between single-qubit coherence and two-qubit entanglement and identify parameter regimes in which the terms robust and fragile are no longer appropriate.