Quantum Repeaters with Encoding on Nitrogen-Vacancy-Center Platforms

We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (N-

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) centers in diamond as quantum memories. N-

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centers offer a two-qubit register, corresponding to their electron and nuclear spins, which makes it possible to perform deterministic two-qubit operations within one N-

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center. For quantum repeater applications, however, we need to do joint operations on two separate N-

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centers. Here, we study two N-

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-center-based repeater structures that enable such deterministic joint operations. One structure offers less consumption of classical communication, at the cost of more computation overhead, whereas the other relies on a smaller number of physical resources and operations. We assess and compare their performance for the task of secret-key generation under the influence of noise and decoherence with current and near-term experimental parameters. We quantify the regimes of operation where one structure outperforms the other, and find the regions where encoded quantum repeaters offer practical advantages over their nonencoded counterparts.