Entanglement in bipartite pure states of an interacting boson gas obtained by local projective measurements

TL;DR

This paper investigates how local projective measurements on a Lieb-Liniger gas can extract entanglement, revealing that entanglement increases with interaction strength and differs fundamentally from free-bosonic systems.

Contribution

It provides the first numerical analysis of entanglement extraction in an interacting boson gas using the Bethe ansatz, highlighting the role of interactions and measurement outcomes.

Findings

Entanglement increases monotonically with repulsive interaction strength.

Maximum entanglement occurs when half the bosons are projected in one partition.

Entanglement in free bosonic systems is zero after projection, unlike in fermionic systems.

Abstract

We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable boson limiting value. We also present evidence indicating that the largest amount of entanglement can be extracted from the most probable projected state having half the number of bosons in a given partition. Our study points to a fundamental difference between the nature of the entanglement in free-bosonic and free-fermionic systems, with the entanglement in the former being zero after projection, while that in the latter (corresponding to the impenetrable boson limit) being non-zero.