Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

TL;DR

This paper demonstrates how to generate high-quality, genuine all-way entangled states in defect-nuclear spin systems using dynamical decoupling sequences, overcoming hyperfine interaction challenges.

Contribution

It introduces the $M$-tangling power concept and shows how to prepare GHZ-like states of up to 10 qubits within coherence time constraints.

Findings

Successfully prepared GHZ$_M$-like states up to M=10 qubits

Developed non-unitary $M$-tangling power to analyze mixed states and errors

High-fidelity state preparation achieved with XY decoupling sequences

Abstract

Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ$_M$-like states with minimal cross-talk. We introduce the $M$-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ$_M$-like states of up to $M=10$ qubits within time constraints that saturate bounds on $M$-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$-tangling power which incorporates the impact of electronic dephasing errors on the $M$-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.