Distance dependence of entanglement generation via a bosonic heat bath

TL;DR

This paper investigates how a bosonic heat bath can generate entanglement between two quantum systems and finds that entanglement is highly sensitive to distance, only occurring at microscopic scales comparable to the interaction's cutoff wavelength.

Contribution

It provides a detailed analysis of the distance dependence of entanglement generation via a bosonic heat bath within a generalized Caldeira-Leggett model.

Findings

Entanglement is exponentially suppressed with distance beyond the cutoff wavelength.

Significant entanglement occurs only at microscopic distances.

Heat baths are ineffective for entangling remote objects.

Abstract

Within a generalized Caldeira-Leggett model we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance $r$. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a {\em microscopic} distance that is of order of the cut-off wavelength $\lambda$ of the system-bath interaction. At larger distances the maximal entanglement is exponentially suppressed with a decay length of order $\lambda$. We conclude that entanglement generation via a heat bath is not suitable for entangling remote objects.