Scalable High-Dimensional Multipartite Entanglement with Trapped Ions

TL;DR

This paper introduces a scalable protocol for generating high-dimensional GHZ states using trapped ions, generalizing the OAT Hamiltonian to qudits, and provides methods for implementation and fidelity certification.

Contribution

It proposes the balanced OAT (BOAT) protocol for creating high-dimensional GHZ states and details specific trapped ion implementations for scalable entanglement generation.

Findings

BOAT protocol successfully generates GHZ states for qutrits and ququarts.

Fidelity thresholds can certify high-dimensional entanglement.

Implementation schemes are feasible with current trapped ion technology.

Abstract

We propose a protocol for the preparation of generalized Greenberger-Horne-Zeilinger (GHZ) states of $N$ atoms each with $d=3$ or $4$ internal levels. We generalize the celebrated one-axis twisting (OAT) Hamiltonian for $N$ qubits to qudits by including OAT interactions of equal strengths between every pair of qudit levels, a protocol we call as balanced OAT (BOAT). Analogous to OAT for qubits, we find that starting from a product state of an arbitrary number of atoms $N$, dynamics under BOAT leads to the formation of GHZ states for qutrits ($d=3$) and ququarts ($d=4$). While BOAT could potentially be realized on several platforms where all-to-all coupling is possible, here we propose specific implementations using trapped ion systems. We show that preparing these states with a fidelity above a threshold value rules out lower dimensional entanglement than that of the generalized GHZ states. For qutrits, we also propose a protocol to bound the fidelity that requires only global addressing of the ion crystal and single-shot readout of one of the levels. Our results open a path for the scalable generation and certification of high-dimensional multipartite entanglement on current atom-based quantum hardware.