Is macroscopic entanglement a typical trait of many-particle quantum states?

TL;DR

This paper explores the relationship between macroscopic quantum entanglement and geometric entanglement, showing that macroscopicity is rare in typical ensembles but common in permutation-symmetric states, despite differences in entanglement.

Contribution

It clarifies the distinction between macroscopicity and geometric entanglement, highlighting their different behaviors in various quantum state ensembles.

Findings

Macroscopicity is rare in uniform and random pure states.

Permutation-symmetric states exhibit strong macroscopicity.

Large geometric entanglement does not imply macroscopicity.

Abstract

We elucidate the relationship between Schr\"odinger-cat-like macroscopicity and geometric entanglement, and argue that these quantities are not interchangeable. While both properties are lost due to decoherence, we show that macroscopicity is rare in uniform and in so-called random physical ensembles of pure quantum states, despite possibly large geometric entanglement. In contrast, permutation-symmetric pure states feature rather low geometric entanglement and strong and robust macroscopicity.