# Generating accessible entanglement in bosons via pair-correlated tunneling

## TL;DR

This paper explores how pair-correlated tunneling in an extended Bose-Hubbard model can generate accessible entanglement, especially after a beamsplitter operation, with potential implications for quantum information processing.

## Contribution

It introduces a minimal four-mode model with pair-correlated tunneling, proposes a variational ground state, and demonstrates entanglement growth and accessibility beyond super-selection constraints.

## Key findings

- Accessible entanglement entropy grows logarithmically with particle number.
- A high fidelity, parameter-free wave function captures ground state features.
- Unitary beamsplitter transforms the ground state into a fully accessible entangled state.

## Abstract

We consider an extended Bose-Hubbard model that includes pair-correlated tunneling. We demonstrate that a minimal four-mode implementation of this model exhibits a pair-correlated regime in addition to Mott insulator and superfluid regimes. We propose a low complexity variational subspace for the ground state of the system in the pair-correlated regime, which we find to be numerically exact in pure pair-tunneling limit. Additionally, we propose a parameter-free high fidelity model wave function that qualitatively captures the features of the ground state in the pair-correlated regime. Although the operationally accessible entanglement vanishes deep inside the Mott insulator and superfluid regimes due to particle number conservation, we find that in the pure pair-correlated tunneling limit the accessible entanglement entropy grows logarithmically with the number of particles. Furthermore, we demonstrate that upon application of a unitary beamsplitter operation, the pair-correlated ground state is transformed into a state with completely accessible entanglement that is not limited by super-selection rules.