Experimental test of Leggett's inequalities with solid-state spins

At a Glance

Metadata	Details
Publication Date	2020-07-09
Journal	Physical review. A/Physical review, A
Authors	Xianzhi Huang, Xiaolong Ouyang, Wenqian Lian, Wengang Zhang, Xin Wang
Institutions	Tsinghua University
Citations	2
Analysis	Full AI Review Included

Executive Summary

This technical analysis summarizes the experimental falsification of Leggett’s Nonlocal Hidden Variable (NLHV) model using solid-state spins, highlighting the critical role of high-quality MPCVD diamond in achieving high-fidelity quantum control.

First Solid-State Test: Reports the first experimental test of Leggett’s NLHV model utilizing a solid-state platform—specifically, the electron spin of a diamond Nitrogen-Vacancy (NV) center entangled with a surrounding ¹³C nuclear spin.
High-Fidelity Entanglement: Achieved a lower bound Bell state fidelity of 98.2(5)%, demonstrating exceptional control over multi-qubit spin registers in diamond.
Significant Violation: Observed clear violation of Leggett-type inequalities (I₂₆ and I₂₈). The maximal violation for the eight-setting inequality (I₂₈) exceeded the classical bound by more than 15.5 standard deviations after readout error correction.
Quantum Control Methodology: Employed dynamical decoupling sequences and optimized quantum gates to protect the nuclear spin from decoherence and achieve the required minimal threshold fidelity (F_min ≈ 97.8%).
Operating Environment: Experiments were conducted at cryogenic temperatures (around 8 K) utilizing optical initialization and single-shot projective readout.
Scientific Impact: The results are in full agreement with quantum mechanics, definitively falsifying Leggett’s NLHV model in a technologically crucial solid-state quantum computing platform.

Technical Specifications

The following table extracts key performance metrics and operational parameters achieved in the experimental test of Leggett’s inequalities.

Parameter	Value	Unit	Context
Quantum Platform	NV Center (e- spin) + ¹³C (nuclear spin)	N/A	Solid-state spins in diamond
Operating Temperature	~8	K	Cryostat environment
Prepared Bell State Fidelity (Lower Bound)	98.2(5)	%	Required for high-confidence violation
Six-Setting Inequality (I₂₆) Classical Bound	6	N/A	Leggett’s NLHV limit
Max Violation (I₂₆, Calibrated Data)	6.382 ± 0.035	N/A	Exceeds bound by >10.9 standard deviations
Optimal Measurement Angle ($\phi_{max}$) for I₂₆	38.96	°	Maximizes quantum violation
Eight-Setting Inequality (I₂₈) Classical Bound	8	N/A	Leggett’s NLHV limit
Max Violation (I₂₈, Calibrated Data)	8.729 ± 0.047	N/A	Exceeds bound by >15.5 standard deviations
Minimal Required Fidelity (I₂₆)	~97.8	%	Threshold required to observe violation
Minimal Required Visibility (I₂₈)	~91.3	%	Threshold required to observe violation

Key Methodologies

The experiment relied on advanced quantum control techniques applied to a high-quality diamond substrate:

Material Selection: Utilized the negative charge state of the NV center (electron spin S=1) coupled to a nearby, weakly coupled ¹³C nuclear spin (I=1/2) within a diamond lattice.
Environmental Control: Maintained the system in a cryostat at approximately 8 K to minimize thermal decoherence effects.
Initialization and Readout: Achieved optical initialization and readout of the electron spin via resonant transitions between excited and ground states.
Hamiltonian Engineering: Applied a magnetic field B_z along the NV symmetry axis to control the effective Hamiltonian, H_eff = A_zzŜ_zÎ_z + A_zxŜ_zÎ_x + $\gamma_{n}$B_zÎ_z, where A_zz and A_zx are hyperfine interaction components.
Gate Construction: Designed and implemented a set of single-qubit gates and electron-nuclear two-qubit entangling gates based on the precisely characterized hyperfine interaction couplings.
Decoherence Protection: Employed dynamical decoupling sequences to construct selective two-qubit gates and protect the single ¹³C nuclear spin from decoherence and crosstalk.
Joint Measurement: Used a combined projective optical readout scheme for simultaneous, single-shot measurement of the electron-nuclear spin state in a rotated basis (e.g., X_eX_n/Y_eY_n).

6CCVD Solutions & Capabilities

The successful replication and extension of this high-coherence quantum experiment fundamentally depends on the quality and customization of the diamond substrate. 6CCVD is uniquely positioned to supply the necessary materials and fabrication services for next-generation solid-state quantum information projects.

Applicable Materials

To achieve the high fidelity (F > 98%) and long coherence times required for NV-based quantum tests, the material must exhibit ultra-low strain and minimal background spin noise.

Optical Grade Single Crystal Diamond (SCD): This is the essential material. 6CCVD provides high-purity SCD with extremely low nitrogen and defect concentrations, crucial for maximizing the coherence time (T₂) of the NV electron spin and the coupled nuclear spins.
Isotopically Purified Diamond (Recommended Extension): Although the paper uses a weakly coupled ¹³C spin, minimizing the natural abundance of ¹³C (1.1%) in the bulk diamond is standard practice to reduce the nuclear spin bath noise. 6CCVD can supply SCD substrates optimized for isotopic purity, enabling even longer coherence times and more robust quantum operations.

Customization Potential

The complexity of NV center experiments requires precise control over substrate geometry and integration of control electronics.

Requirement from Paper	6CCVD Customization Service	Technical Benefit
Specific Crystal Orientation/Size	Custom Dimensions & Thickness	6CCVD supplies SCD plates/wafers up to 125mm, with thicknesses ranging from 0.1µm to 500µm, allowing researchers to optimize NV depth and device integration.
High-Fidelity Optical Access	Ultra-Polishing (Ra < 1nm)	Our SCD substrates are polished to an atomic scale (Ra < 1nm), minimizing surface defects and scattering losses critical for high-efficiency optical initialization and readout at 8 K.
Microwave/RF Control Integration	Custom Metalization Services	We offer in-house deposition of standard and custom metal stacks (Au, Pt, Pd, Ti, W, Cu) directly onto the diamond surface for fabricating microwave strip lines, antennas, and ohmic contacts necessary for spin manipulation.
Scaling and Integration	Large Area PCD Substrates	For future generalizations to multi-qubit arrays or integrated quantum circuits, 6CCVD offers large-area Polycrystalline Diamond (PCD) substrates up to 125mm, polished to Ra < 5nm.

Engineering Support

The successful implementation of dynamical decoupling and complex Hamiltonian control (Eq. 3) requires deep expertise in diamond material science and quantum physics.

Material Selection Consultation: 6CCVD’s in-house PhD team specializes in material selection for advanced quantum applications, including optimizing NV creation, managing strain, and selecting the appropriate isotopic purity for similar Solid-State Quantum Information projects.
Fabrication Expertise: We provide technical support on post-processing steps, including precise laser cutting and etching, ensuring the final diamond geometry meets the stringent requirements for microwave delivery and optical access.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. Global shipping (DDU default, DDP available) ensures timely delivery of critical quantum materials worldwide.

View Original Abstract

Bell’s theorem states that no local hidden variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett’s nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled $^{13}C$ nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett’s nonlocal hidden variable inequality with a high level of confidence.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.102.012210

References

2004 - Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy [Crossref]