Heralded interconversion between hyperentangled W state and hyperentangled KLM state assisted by nitrogen vacancy centers coupled with microresonators
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2025-01-20 |
| Journal | Scientific Reports |
| Authors | Fang‐Fang Du, Ming Ma, Qiulin Tan |
| Institutions | North University of China |
| Citations | 11 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This paper presents novel protocols for the deterministic and complete mutual interconversion between two critical hyperentangled states: the W state and the Knill-Laflamme-Milburn (KLM) state, utilizing a hybrid quantum system.
- Core Value Proposition: Realization of deterministic, high-fidelity mutual conversion between hyperentangled W and KLM states, encoded concurrently in both polarization and spatial degrees of freedom (DoFs).
- Hybrid System: The protocol relies on the practical nonlinear interaction provided by Nitrogen-Vacancy (NV) centers in diamond coupled with Whispering-Gallery-Mode (WGM) microresonators.
- Key Achievement (Fidelity): The conversion fidelity theoretically approaches unity due to the use of error-heralded quantum control gates (BLOCK modules). Errors from imperfect coupling or scattering are translated into detectable signals, allowing for heralded failure rather than state corruption.
- Key Achievement (Efficiency): High conversion efficiencies are achieved, reaching up to 95.96% through optimization of coupling parameters and the use of iterative conversion steps for the KLM-to-W process.
- Gate Implementation: The conversion relies fundamentally on hyperparallel quantum control gates, specifically the hyperparallel Controlled-NOT (CNOT) and Controlled-SWAP (Fredkin) gates.
- Significance: The protocols enhance the understanding and exploitation of hyperentanglement properties, paving the way for more robust and efficient Quantum Information Technologies (QITs).
Technical Specifications
Section titled “Technical Specifications”The following specifications detail the performance and operational parameters of the NV-WGM hybrid system used for the hyperentanglement conversion protocols.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| NV Center Ground State Splitting | 2.87 | GHz | Energy difference between |
| Target Conversion Fidelity | ~1 | (Unity) | Achieved in principle due to error-heralding (BLOCK modules). |
| Strong Coupling Condition | g2/(κγ) > 1 and κ > κs | Dimensionless | Required for effective NV-WGM interaction (g: coupling strength, κ: coupling rate, γ: decay rate, κs: side-leakage rate). |
| Optimal Coupling Ratio (g/κ) | 4.4 | Dimensionless | Maximizes conversion efficiency (e.g., η reaches 95.96%). |
| Dipole-Decay Rate Ratio (γ/κ) | 0.1 | Dimensionless | Used for efficiency calculations in Fig. 5. |
| Resonator Leakage Ratio (κs/κ) | 0 | Dimensionless | Ideal condition for maximum efficiency. Efficiency drops significantly if κs/κ increases (e.g., to 69.94% at κs/κ = 0.05). |
| W to KLM Conversion Efficiency (η) | 87.08% | % | Calculated at g/κ = 2.4, κs/κ = 0, γ/κ = 0.1. |
| KLM to W Conversion Efficiency (η1) | 80.91% | % | Initial efficiency (g/κ = 2.4, κs/κ = 0, γ/κ = 0.1). |
| KLM to W Efficiency (η3) | 90.01% | % | Efficiency after the second iteration (g/κ = 2.4, κs/κ = 0, γ/κ = 0.1). |
| Phase-Flip Operation (Polarization) | σz = | R><R | - |
Key Methodologies
Section titled “Key Methodologies”The conversion protocols rely on a sequence of interactions between photons (qubits) and NV-center electron spins (auxiliary qubits) mediated by WGM microresonators.
-
Hybrid System Setup:
- A negatively charged NV center in diamond is affixed to the exterior surface of a microtoroidal WGM resonator.
- The resonator is coupled to two tapered optical fibers, providing four ports (a1, a2, b1, b2) for photon input/output.
- The system operates in the strong-coupling regime (g2/(κγ) > 1) to ensure deterministic interaction rules.
-
Error-Heralded Quantum Gates (BLOCKs):
- Linear optical elements (CPBSs, partial transmission mirror T, BSs, wave plates H, X) are used in conjunction with the NV-resonator system to construct two error-heralded modules: BLOCK1 and BLOCK2.
- These modules function as controlled-phase or controlled-bit-flip gates between the photon polarization/spatial DoFs and the NV electron spin.
- Single-photon detectors (D1, D2) are strategically placed to herald errors arising from imperfect photon-spin interaction or non-ideal partial transmission, ensuring high fidelity.
-
W State to KLM State Conversion Protocol:
- The three-photon W state (|Φ>) is initialized along with two NV centers (NV1, NV2) in the state |φ>+.
- Photons A and B interact sequentially with BLOCK1 (NV1) and BLOCK2 (NV2).
- The electron spins (NV1, NV2) are measured in the Hadamard basis, yielding four possible outcomes.
- Based on the measurement results, specific feedback operations (Hadamard, phase-flip Z, bit-flip X, swap S) are applied to the photons.
- The photons then pass through a Hyper-Fredkin gate (encoding photon B as control) to complete the transformation to the KLM state (|Φ>).
-
KLM State to W State Conversion Protocol (Iterative):
- The KLM state (|Φ>) is initialized along with four NV centers (NV5, NV6, NV7, NV8).
- The initial conversion steps involve interactions with BLOCK1 (NV5) and BLOCK2 (NV6), followed by measurement of NV5 and NV6.
- Feedback operations are applied, and the photons pass through the Hyper-Fredkin gate.
- Subsequent steps involve interaction with BLOCK1 (NV7) and BLOCK2 (NV8), followed by measurement of NV7 and NV8.
- Finally, the photons pass through a Hyper-CNOT gate (encoding photon C as control) to achieve the W state (|ψ>). The iterative nature (Loop) allows for reusing heralded failures to boost overall efficiency.
Commercial Applications
Section titled “Commercial Applications”This research directly supports the advancement of next-generation Quantum Information Technologies (QITs) by providing robust methods for manipulating complex entangled states.
- Scalable Quantum Computing:
- The deterministic, high-fidelity hyperparallel gates (Fredkin and CNOT) are fundamental building blocks for scalable quantum circuits, particularly those utilizing photonic qubits encoded in multiple DoFs.
- The ability to interconvert W states (robust against particle loss, useful for fault tolerance) and KLM states (high resilience against specific errors) allows for flexible algorithm design and error correction.
- High-Capacity Quantum Networks:
- Hyperentanglement significantly enhances channel capacity and noise resistance compared to single-DoF entanglement, enabling faster and more secure quantum communication links.
- The NV-WGM system provides a solid-state platform suitable for integration into quantum repeaters and network nodes.
- Fault-Tolerant Quantum Systems:
- The W state’s inherent robustness against particle loss makes it ideal for distributing entanglement across noisy quantum channels. The conversion protocol ensures that this robust state can be generated and utilized efficiently.
- Quantum Error Correction (QEC):
- The KLM state is strategically important for QEC codes. The ability to convert other states into the KLM state deterministically provides a necessary resource for empowering error detection and correction during QIT processes.