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arXiv · 2407.19735

Scalable High-Dimensional Multipartite Entanglement with Trapped Ions

Harsh Vardhan Upadhyay·Sanket Kumar Tripathy·Ting Rei Tan·Baladitya Suri·Athreya Shankar
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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.

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Harsh Vardhan Upadhyay, Sanket Kumar Tripathy, Ting Rei Tan, Baladitya Suri, Athreya Shankar. 2024-07-29. Scalable High-Dimensional Multipartite Entanglement with Trapped Ions. https://arxiv.org/abs/2407.19735

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