Quantum Repeaters with Encoding on Nitrogen-Vacancy-Center Platforms
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-08-16 |
| Journal | Physical Review Applied |
| Authors | Yumang Jing, Mohsen Razavi |
| Institutions | University of Leeds |
| Citations | 5 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis analysis investigates the feasibility and performance of quantum repeater (QR) protocols utilizing Nitrogen-Vacancy (NV) centers in diamond, benchmarked against Quantum Key Distribution (QKD) rates.
- Core Technology: NV centers serve as two-qubit registers (electron spin for optical interface, nuclear spin for long-term storage), enabling deterministic two-qubit gates crucial for encoded QRs.
- Architectural Comparison: Two encoded QR structures (Protocol 1: fully encoded, higher overhead; Protocol 2: partially encoded, fewer resources) were compared against uncoded counterparts (P3, P4).
- Performance Advantage: Encoded QRs (P1, P2) are necessary for long-distance communication (Ltot > 100 km), significantly outperforming uncoded schemes which are limited by low error tolerance.
- Optimal Protocol: Protocol 2 (partially encoded) consistently offers the highest normalized Secret Key Rate (SKR) across most practical regimes, requiring fewer NV centers and operations than Protocol 1.
- Decoherence Sensitivity: System performance is highly sensitive to memory coherence times (Te and Tn). Achieving distances over 2000 km requires Te = 100 ms and Tn = 10 s, demonstrating the need for continued memory improvement.
- Practical Conclusion: For near-term experimental implementations, the partially encoded QR structure (P2) is the most practical and efficient choice, balancing resource consumption with robust error detection capabilities.
Technical Specifications
Section titled âTechnical SpecificationsâThe following parameters were used in the numerical simulations, reflecting current and near-term experimental capabilities of NV center platforms.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Electron Spin Coherence Time (Te) | 10 | ms | Nominal/Current practical value |
| Nuclear Spin Coherence Time (Tn) | 1 | s | Nominal/Current practical value |
| Improved Te (Projected) | 100 | ms | Required for long-distance scaling (e.g., 2000 km) |
| Improved Tn (Projected) | 10 | s | Required for long-distance scaling (e.g., 2000 km) |
| CNOT Gate Error Probability (Beta) | 10-3 | - | Nominal error rate used in analysis |
| Electron Measurement Error (Delta) | 10-4 | - | Assumed high-fidelity measurement |
| Single-Photon Detector Efficiency (Etad) | 0.9 | - | Assumed high-efficiency superconducting detectors |
| Coupling Efficiency (Etac) | 0.3 to 0.5 | - | Range studied for ZPL photon collection |
| Attenuation Length (Latt) | 22 | km | Standard optical fiber characteristic |
| Speed of Light in Fiber (c) | 2 x 105 | km/s | Channel transmission speed |
| Optimum Inter-Node Distance (L0) | 5 to 20 | km | Varies based on total distance and nesting level (n) |
| Maximum Distance (Ltot) | 2000 | km | Achievable with improved coherence times |
Key Methodologies
Section titled âKey MethodologiesâThe study relies on analytical modeling of four distinct QR protocols (P1, P2, P3, P4) implemented on NV center platforms, focusing on deterministic operations and robust error modeling.
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Elementary Link Entanglement Distribution:
- Bell pairs (Phi+) are generated between remote electron spins using a generic two-mode spin-photon interference scheme.
- The electron spin state is immediately mapped and stored onto the corresponding nuclear spin (the long-term memory).
- The success probability (P0) depends on ZPL emission, collection efficiency (Etac), detector efficiency (Etad), and fiber transmissivity (Etat).
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Encoded Entanglement Generation (P1, P2):
- The three-qubit repetition code (logical 0 = 000, logical 1 = 111) is used for error detection.
- Encoded Bell states (Phi+)AB are created using transversal remote CNOT gates, which require pre-existing Bell pairs between the electron spins of the two remote NV centers.
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Entanglement Swapping (ES) and Distillation:
- ES is performed deterministically at intermediate nodes.
- For joint measurements on nuclear spins, an auxiliary Bell pair is first established between the corresponding electron spins.
- BSMs are then performed locally within each NV center (nuclear spin to electron spin mapping followed by electron spin measurement).
- Error detection is achieved by post-selecting only those ES outcomes that indicate no bit-flip errors (majority rule is not used).
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Comprehensive Error Modeling:
- Gate Errors: CNOT operations are modeled using a uniform depolarization channel (parameter Beta).
- Measurement Errors: Projective measurements on electron spins are modeled with error probability Delta.
- Decoherence: Both electron (Te) and nuclear (Tn) spins are modeled using independent depolarizing channels, calculated based on the average waiting time (T1 or T2) for each stage of the protocol.
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Performance Calculation:
- The final shared state (rhofinal) is calculated accounting for all operational errors and decoherence effects.
- The Secret Key Rate (R) is derived from the secret fraction (rinfinity) of the BBM92 QKD protocol, multiplied by the entanglement generation rate (Ps / (T1 + T2)).
- Results are normalized by the total number of NV centers used to compare architectural efficiency.
Commercial Applications
Section titled âCommercial ApplicationsâThe research focuses on optimizing quantum communication infrastructure using solid-state qubits, directly impacting the development and scaling of quantum networks.
- Long-Haul Quantum Networks: The primary application is enabling secure, high-rate QKD over continental distances (up to 2000 km projected) by overcoming exponential fiber loss.
- Solid-State Quantum Memory Modules: NV centers provide the necessary two-qubit register (electron/nuclear spin) for high-fidelity quantum storage, essential for buffering and synchronization in complex quantum network nodes.
- Deterministic Quantum Gates: The reliance on deterministic CNOT and controlled phase gates within the NV center is a key requirement for fault-tolerant quantum computing architectures based on solid-state platforms.
- Integrated Quantum Repeaters (Generation 2.5/3): This work provides a blueprint for building partially encoded QRs (Protocol 2), which are more resource-efficient than fully encoded schemes and offer a practical path toward scalable quantum internet infrastructure.
- High-Fidelity Diamond Material Production: The success of these protocols depends critically on high-quality diamond substrates with long coherence times (Tn > 10 s), driving demand for advanced CVD growth techniques optimized for low-strain and high-purity material.
View Original Abstract
We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV 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 NV center. For quantum repeater applications, we, however, need to do joint operations on two separate NV centers. Here, we study two NV-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 one relies on a fewer 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 non-encoded counterparts.