Improved entanglement detection with subspace witnesses
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-01-13 |
| Journal | Physical review. A/Physical review, A |
| Authors | Won Kyu Calvin Sun, A. R. COOPER, Paola Cappellaro |
| Institutions | University of Waterloo, Massachusetts Institute of Technology |
| Citations | 11 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Improved Entanglement Detection in Diamond Qubits
Section titled “Technical Documentation & Analysis: Improved Entanglement Detection in Diamond Qubits”Executive Summary
Section titled “Executive Summary”This research successfully demonstrates a robust method for detecting quantum entanglement in a solid-state diamond platform, utilizing a novel “subspace witness” (Ws) metric. This approach is highly relevant for scaling quantum processors and mitigating common experimental errors.
- Platform Validation: Entanglement was successfully generated and detected in a solid-state two-qubit system based on electronic spin impurities (Nitrogen-Vacancy (NV) center and a dark spin) in diamond.
- Improved Robustness: The subspace witness (Ws) provides significantly improved entanglement detection compared to the conventional state witness (Wψ), achieving a violation of -0.1827(4) versus -0.07421(4).
- Error Mitigation: Ws is inherently insensitive to local unitary errors during State Preparation and Measurement (SPAM), which typically plague fidelity-based measurements.
- Coherence Quantification: The method allows for the direct identification and quantification of the true (maximum) many-body coherences, which are critical for applications like entanglement-enhanced sensing.
- Material Requirement: The experiment relies on high-purity, low-defect Single Crystal Diamond (SCD) to maintain long coherence times (T2 = 31 µs) necessary for complex quantum gates (HHCP).
- Scalability: The efficient measurement protocol (requiring only 3 measurements for two qubits, scaling favorably for GHZ states) is highly beneficial for characterizing noisy, intermediate-scale quantum (NISQ) processors.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Subspace Witness Violation (Ws) | -0.1827(4) | Dimensionless | Optimized Bell subspace fidelity |
| State Witness Violation (Wψ) | -0.07421(4) | Dimensionless | Conventional Bell state fidelity |
| Decoherence Time (T2) | 31(3) | µs | Fitted to Gaussian decay of double-quantum coherence |
| Characteristic Decay Time (T) | 25 | µs | Fitted to exponential decay of two-body correlators |
| Entanglement Threshold (τ*) | 33(3) | µs | Time until entanglement is no longer witnessed |
| Population (P) | 0.371(1) | Dimensionless | Constant over the timescale of the experiment |
| Entangling Gate Time (dt) | π/4 | Radians/d | Realizes the √iSWAP gate via HHCP |
| Measurement Modulation (ν) | 15 | kHz | Used for phase rotation (φ = ντ) in spin echo |
| Maximum Fidelity (Fs) | 0.6827(4) | Dimensionless | Maximized over the Bell subspace |
Key Methodologies
Section titled “Key Methodologies”The experimental generation and detection of entanglement were performed using a solid-state two-qubit system hosted in diamond.
- Material System: Utilized a hybrid two-qubit system comprising an NV center electronic spin and a nearby, optically dark electronic spin-1/2 defect in Single Crystal Diamond (SCD).
- State Initialization (I):
- The system was initialized to the thermal equilibrium state (ρ0) using a Maxwell demon-type cooling scheme.
- The NV spin was initialized to a high-purity state using spin non-conserving optical transitions under laser illumination.
- The NV state was then swapped with the dark electronic spin (X) to complete the initialization (I).
- Entanglement Generation (U):
- The entangling operation (U) was achieved using Hartmann-Hahn Cross-Polarization (HHCP), exploiting the spin coupling (Hint = dσz1σz2/2).
- HHCP involved driving both spins with two-tone microwave pulses, tuned to resonance in the dressed basis by adjusting driving strengths (Ω) and frequencies (δω).
- Specific driving times (e.g., dt = π/4) were used to realize conditional gates like √iSWAP.
- State Witness Measurement (Wψ):
- Wψ was measured by reconstructing the Bell state fidelity (Fψ) using three two-body correlators: <σx1σx2>, <σy1σy2>, and <σz1σz2>.
- Correlators were obtained by evolving the state under a CNOT gate (realized via Hint and collective rotations) and measuring the NV center state (M = |0><0|).
- Subspace Witness Measurement (Ws):
- Ws was obtained by maximizing the fidelity over the relevant entangled subspace, requiring multiple fidelity measurements to extract the coherence magnitude (|ρkk|).
- This was achieved by sweeping the effective control phase (φ) or by measuring the phase-modulated decay of the coherence using a spin echo sequence of varying duration (τ).
6CCVD Solutions & Capabilities
Section titled “6CCVD Solutions & Capabilities”The successful implementation of robust quantum protocols using diamond defects, as demonstrated in this paper, relies fundamentally on the quality and engineering of the diamond substrate. 6CCVD is uniquely positioned to supply the materials and customization required to replicate and advance this research.
Applicable Materials
Section titled “Applicable Materials”To host stable, high-coherence NV centers and other electronic defects necessary for this two-qubit system, the researchers require ultra-high purity, low-strain Single Crystal Diamond (SCD).
| 6CCVD Material | Specification | Relevance to Research |
|---|---|---|
| Optical Grade SCD | Nitrogen concentration < 1 ppb; Low Birefringence | Essential for long T2 coherence times (31 µs achieved) and minimizing spectral diffusion, crucial for stable NV operation. |
| Custom SCD Substrates | Thickness: 0.1 µm to 500 µm | Precise thickness control is vital for efficient optical coupling (laser illumination) and integration with microwave circuitry. |
| NV-Engineered Diamond | Post-growth implantation/annealing services | We offer services to create specific defect densities (e.g., NV centers) necessary for controlled two-qubit interactions with nearby dark spins. |
Customization Potential
Section titled “Customization Potential”The experimental setup requires precise integration of microwave control and optical access. 6CCVD’s in-house engineering capabilities directly address these needs:
- Custom Dimensions: While the paper does not specify dimensions, 6CCVD can supply SCD plates and wafers up to 125 mm (PCD) and custom-cut SCD pieces, ensuring compatibility with existing cryostat and microwave setups.
- Metalization Services: The HHCP and measurement protocols rely on delivering precise microwave pulses. 6CCVD offers internal metalization capabilities (Au, Pt, Ti, W, Cu) for fabricating on-chip microwave structures (e.g., coplanar waveguides) directly onto the diamond surface, improving coupling efficiency and control fidelity.
- Example: We can deposit a Ti/Pt/Au stack for robust, low-loss microwave delivery.
- Polishing: Achieving high-fidelity optical initialization requires excellent surface quality. 6CCVD guarantees Ra < 1 nm polishing for SCD, ensuring minimal scattering losses and optimal optical access to the NV layer.
Engineering Support
Section titled “Engineering Support”The successful implementation of the subspace witness requires deep knowledge of defect physics, quantum control sequences (like HHCP), and robust measurement protocols.
- QIP Consultation: 6CCVD’s in-house PhD team specializes in material selection and optimization for solid-state quantum computing and sensing applications. We can assist researchers in selecting the optimal SCD grade and defect engineering recipe for similar NV-based entanglement detection projects.
- Global Logistics: We provide reliable global shipping (DDU default, DDP available) to ensure sensitive, custom-engineered diamond substrates reach your lab efficiently and safely, minimizing delays in critical research timelines.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Entanglement, while being critical in many quantum applications, is difficult\nto characterize experimentally. While entanglement witnesses based on the\nfidelity to the target entangled state are efficient detectors of entanglement,\nthey in general underestimate the amount of entanglement due to errors during\nstate preparation and measurement. Therefore, to detect entanglement more\nrobustly in the presence of such control errors, we introduce a ‘subspace’\nwitness that detects a broader class of entangled states with strictly larger\nviolation than the conventional state-fidelity witness at the cost of\nadditional measurements, while remaining more efficient with respect to state\ntomography. We experimentally demonstrate the advantages of the subspace\nwitness by generating and detecting entanglement with a hybrid, two-qubit\nsystem composed of electronic spins in diamond. We further extend the notion of\nsubspace witness to specific genuine multipartite entangled (GME) states such\nas GHZ, W, and Dicke states, and motivate the choice of the metric based on\nquantum information tasks such as entanglement-enhanced sensing. In addition,\nas the subspace witness identifies the many-body coherences of the target\nentangled state, it facilitates (beyond detection) lower-bound quantification\nof entanglement via generalized concurrences. We expect the straightforward and\nefficient implementation of subspace witnesses would be beneficial in detecting\nspecific GME states in noisy, intermediate-scale quantum processors with a\nhundred qubits.\n
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
Section titled “References”- 2016 - International Conference on Micro- and Nano-Electronics 2016
- 2019 - International Conference on Micro- and Nano-Electronics 2018