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arXiv:2105.14122 · Physical Review Applied

Quantum Repeaters with Encoding on Nitrogen-Vacancy-Center Platforms

Yumang Jing, Mohsen Razavi

Published Aug 16, 2022• 11 citations
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Abstract

We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (N-$V$) centers in diamond as quantum memories. N-$V$ 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-$V$ center. For quantum repeater applications, however, we need to do joint operations on two separate N-$V$ centers. Here, we study two N-$V$-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.

DOI
10.1103/physrevapplied.18.024041

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We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (N-VVV) centers in diamond as quantum memories. N-VVV 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-VVV center. For quantum repeater applications, however, we need to do joint operations on two separate N-VVV centers. Here, we study two N-VVV-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.
Quantum channels enable the implementation of communication tasks inaccessible to their classical counterparts. The most famous example is the distribution of secret key. However, in the absence of quantum repeaters, the rate at which these tasks can be performed is dictated by the losses in the quantum channel. In practice, channel losses have limited the reach of quantum protocols to short distances. Quantum repeaters have the potential to significantly increase the rates and reach beyond the limits of direct transmission. However, no experimental implementation has overcome the direct transmission threshold. Here, we propose three quantum repeater schemes and assess their ability to generate secret key when implemented on a setup using nitrogen-vacancy (NV) centers in diamond with near-term experimental parameters. We find that one of these schemes---the so-called single-photon scheme, requiring no quantum storage---has the ability to surpass the capacity---the highest secret-key rate achievable with direct transmission---by a factor of 7 for a distance of approximately 9.2 km with near-term parameters, establishing it as a prime candidate for the first experimental realization of a quantum repeater.
We study the implementation of quantum-key-distribution (QKD) systems over quantum-repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only aid system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three- and five-qubit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters—based on simple three-qubit repetition codes—could offer practical advantages.
We study the implementation of quantum-key-distribution (QKD) systems over quantum-repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only aid system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three- and five-qubit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters---based on simple three-qubit repetition codes---could offer practical advantages.
Future quantum networks will enable the realisation of a large family of quantum protocols, hence allowing for implementation of various tasks ranging from quantum cryptography through quantum computing to quantum metrology.In this thesis we analyse and develop the building blocks of quantum repeater networks.These networks consist of quantum repeater nodes, which are equipped with quantum memories enabling storage of quantum information.The repeater nodes are connected using optical fibres that enable for the transmission of photonic quantum signals between the repeater nodes.We specifically focus on the two building blocks: remote entanglement generation and entanglement distillation.We then investigate various proof of principle quantum repeater schemes used for generating shared secret key between distant parties.The repeater schemes that we consider utilise one to three memory nodes capable of generating memory-photon entanglement.Finally, we introduce a novel framework for investigating a foundational aspect in the use of quantum communication related to the uncertainty principle.Efficient remote entanglement generation is an indispensable building block of most near-term quantum repeater networks.In this thesis we consider various remote entanglement generation schemes that permit multiplexing, which aims at increasing the throughput of this procedure.We find that for the specific schemes that are suitable for platforms with a single communication qubit and multiple memory qubits, the performance of the multiplexing approach is strongly dependent on the time it takes to perform local operations within the memory nodes.Entanglement distillation enables for filtering out the noise from imperfect entangled states using only local operations and classical communication.Using a general framework for optimising such schemes, which we have developed, we have proven optimality of specific generic and experimentally relevant distillation schemes.We have developed a general framework for optimising such schemes, which we have used to prove optimality of various generic and experimentally relevant distillation schemes.In designing proof of principle quantum repeater schemes we assume an informationtheoretic approach, which enables us to assess their performance in a hardware-agnostic way.We find that all the schemes that we consider can prove useful in specific parameter regimes for the nitrogen-vacancy centre platform.Moreover, we find that one scheme which has already been realised experimentally in the context of remote entanglement generation, is expected to significantly outperform every possible system based on direct communication without repeaters.However, our analysis shows that encapsulating the nitrogen-vacancy centres in optical cavities for the enhancement of the emission rates is a necessary requirement for such a successful demonstration of the first proofof-principle quantum repeater.xi xii SUMMARY Finally, we investigate the quantum uncertainty principle which is a fundamental feature of quantum mechanics, allowing for security in many quantum cryptographic protocols.We find that in a particular scenario, relevant from the perspective of quantum key distribution, a significant part of the observed uncertainty is in fact due to lack of information rather than intrinsic.If the eavesdropper could access that information, she would be able to much better, or in some cases even with certainty, guess the value of the raw bit of the generated key.
We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the trade-off in the secret key rate between the communication time and the required resources. For this purpose we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given by L. Jiang et al. [Phys. Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in the encoded connection procedure of this repeater and develop a suitable decoding algorithm. Furthermore, we derive the rate of producing entangled pairs for the quantum repeater using encoding and give the minimal parameter values (gate quality and initial fidelity) for establishing a nonzero secret key. We find that the generic quantum repeater is optimal regarding the secret key rate per memory per second and show that the encoded quantum repeater using the simple three-qubit repetition code can even have an advantage with respect to the resources compared to other recent quantum repeater schemes with encoding.
The realization of a network of quantum registers is an outstanding challenge in quantum science and technology.We experimentally investigate a network node that consists of a single nitrogen-vacancy center electronic spin hyperfine coupled to nearby nuclear spins.We demonstrate individual control and readout of five nuclear spin qubits within one node.We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical internode entangling protocol.We find that the storage fidelity is limited by dephasing during the electronic spin reset after failed attempts.By encoding quantum states into a decoherence-protected subspace of two nuclear spins, we show that quantum coherence can be maintained for over 1000 repetitions of the remote entangling protocol.These results and insights pave the way towards remote entanglement purification and the realization of a quantum repeater using nitrogen-vacancy center quantum-network nodes.