Scalable High-Dimensional Multipartite Entanglement with Trapped Ions

• URL: http://arxiv.org/abs/2407.19735v1
• Date: Mon, 29 Jul 2024 06:54:50 GMT
• Title: Scalable High-Dimensional Multipartite Entanglement with Trapped Ions
• Authors: Harsh Vardhan Upadhyay, Sanket Kumar Tripathy, Ting Rei Tan, Baladitya Suri, Athreya Shankar,
• Abstract summary: We generalize the celebrated one-axis twisting (OAT) Hamiltonian for $N$ qubits to qudits. 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 and ququarts. Our results open a path for the scalable generation and certification of high-dimensional multipartite entanglement on current atom-based quantum hardware.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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