Direct measurement of nonlocal entanglement of two-qubit spin quantum states

At a Glance

Metadata	Details
Publication Date	2016-01-18
Journal	Scientific Reports
Authors	Liu‐Yong Cheng, Guo-Hui Yang, Qi Guo, Hong‐Fu Wang, Shou Zhang
Institutions	Shanxi Normal University, Yanbian University
Citations	11
Analysis	Full AI Review Included

Technical Documentation & Analysis: Direct Entanglement Measurement via NV Centers in Diamond

This documentation analyzes the requirements and achievements of the research paper, “Direct measurement of nonlocal entanglement of two-qubit spin quantum states,” and maps them directly to the specialized capabilities of 6CCVD’s MPCVD diamond products.

Executive Summary

The research demonstrates a robust, non-demolition method for quantifying quantum entanglement (concurrence) in solid-state systems, leveraging the unique properties of Nitrogen-Vacancy (NV) centers in diamond.

Core Platform: Utilizes electron spin states of NV centers embedded in diamond microcavities (Microtoroidal Resonators, MTRs) as the primary solid-state qubits.
Measurement Technique: Achieves direct concurrence measurement by monitoring the detection probability of auxiliary single-photon pulses interacting with the NV centers, eliminating the need for complex joint inter-qubit operations.
Non-Demolition Principle: The measurement process avoids complete annihilation of the initial entangled particle-pair, instead collapsing them into maximally entangled multi-qubit GHZ states suitable for subsequent quantum processing.
Relaxed Experimental Constraints: High reflection coefficients ($r(\omega_p) \approx 0.95$) are achieved even under weak coupling conditions ($g \approx 0.01\kappa$), significantly reducing the requirement for strong coupling or high-quality resonators.
Material Requirement: The scheme relies critically on the long electron spin coherence time (milliseconds, even at room temperature) inherent to high-quality, isotopically engineered Single Crystal Diamond (SCD).
Universal Applicability: Schemes are presented for measuring concurrence in both two-qubit pure states (Bell-like, arbitrary states) and mixed states (Collins-Gisin state).

Technical Specifications

The following hard data points and operational parameters were extracted from the analysis of the proposed schemes:

Parameter	Value	Unit	Context
NV Center Qubit States	$	-1\rangle$ and $	+1\rangle$
Ideal Reflectance ($r(\omega_p)$)	1	N/A	Required for perfect controlled phase flip gate
Achieved Reflectance (Weak Coupling)	$\approx 0.95$	N/A	Verified at $g/\kappa \approx 0.01$
Minimum Coupling Ratio ($g/\kappa$)	$\approx 0.01$	N/A	Sufficient for high-fidelity interaction
Maximum Side Leak Rate Ratio ($\kappa_s/\kappa$)	$\approx 0.02$	N/A	Ensures valid coupled/decoupled reflectances
Cavity Decay Rate ($\gamma$)	$1.5 \times 10^{-5}\kappa$	N/A	Used in reflectance verification
Electron Spin Coherence Time ($T$)	ms	milliseconds	Required to ensure sufficient operating time between sequential photon pulses
Concurrence Formula (Pure State)	$C(	\Psi\rangle) = \sqrt{2P}$	N/A
Photon Generation Rate (Cited)	300,000	photons/30s	Current experimental capability

Key Methodologies

The direct measurement of concurrence relies on a controlled phase flip gate implemented via the interaction between a single-photon pulse and the NV center spin state within a microtoroidal resonator (MTR).

System Preparation: NV centers are fixed onto the surface of a high-quality diamond substrate coupled to an optical microcavity (MTR). The NV center spin is initialized in a superposition state.
Qubit Encoding: The NV center electron spin ground states $|-1\rangle$ and $|+1\rangle$ are used as the qubit basis.
Photon Interaction: A single polarized photon pulse (e.g., $|L\rangle$ or $|R\rangle$) is introduced into the MTR cavity mode, resonant with the NV center transition ($\omega_e = \omega_c = \omega_p$).
Controlled Phase Flip (CPF): Due to optical Faraday rotation, the output photon experiences a phase shift dependent on the NV spin state. By applying a $\pi$ phase shifter to the reflection path, a CPF gate is realized:
- $|R\rangle|\pm 1\rangle \to |R\rangle|\pm 1\rangle$
- $|L\rangle|+1\rangle \to |L\rangle|+1\rangle$
- $|L\rangle|-1\rangle \to -|L\rangle|-1\rangle$ (Phase flip)
Entanglement Evolution: Two pairs of entangled NV centers (or photons) are sequentially interacted with auxiliary single-photon pulses, collapsing the four-qubit system into a Greenberger-Horne-Zeilinger (GHZ) state.
Concurrence Extraction: The polarization state of the output photon is detected. The probability $P$ of detecting a specific output state (e.g., $(|R\rangle - |L\rangle)/\sqrt{2}$) is measured, and the concurrence $C$ is calculated directly from $P$.
Arbitrary State Measurement: For arbitrary two-qubit pure states, additional operations are required, including the sequential use of three single-photon pulses and the application of Hadamard operators (implemented via microwave pulses) on the NV centers.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-purity, high-quality diamond substrates to realize scalable solid-state quantum information processing. 6CCVD is uniquely positioned to supply the specialized materials required to replicate and advance these NV-center-based entanglement schemes.

Applicable Materials

To achieve the long electron spin coherence times ($T$) required (ms range) and minimize decoherence effects, the research demands the highest quality material:

Application Requirement	6CCVD Material Recommendation	Technical Rationale
Long Spin Coherence ($T$)	Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen concentration (Type IIa equivalent) minimizes paramagnetic defects, maximizing $T_2^*$ and $T_2$ coherence times essential for high-fidelity qubit operation.
Microcavity Integration	High-Purity Polycrystalline Diamond (PCD)	Available in large formats (up to 125 mm) for scalable fabrication of MTR arrays or integrated photonic circuits.
Electrical/Microwave Control	Boron-Doped Diamond (BDD)	Can be used for integrated electrodes or sensors, providing conductive pathways for microwave pulses required for Hadamard gates and spin manipulation.

Customization Potential

The integration of NV centers with microcavities necessitates precise material specifications and surface engineering, areas where 6CCVD excels:

Research Need	6CCVD Customization Service	Specification Range
Substrate Dimensions	Custom Plate/Wafer Fabrication	Plates/wafers up to 125 mm (PCD); Substrates up to 10 mm thick.
Surface Quality	Ultra-Smooth Polishing	Ra < 1 nm (SCD) and Ra < 5 nm (Inch-size PCD), critical for low-loss optical coupling to MTRs.
Thickness Control	Precision Thickness Control	SCD and PCD layers available from 0.1 µm to 500 µm, allowing optimization for microcavity coupling depth.
Ancillary Circuitry	Custom Metalization	Internal capability to deposit Au, Pt, Pd, Ti, W, and Cu contacts for integrated microwave control lines and electrical readout.

Engineering Support

The successful implementation of these direct concurrence measurement schemes requires careful material selection to balance optical quality, spin coherence, and integration feasibility.

6CCVD’s in-house PhD team can assist researchers and engineers with material selection and optimization for similar Solid-State Quantum Information and Computation projects. We provide consultation on:

Optimizing nitrogen concentration for desired NV center density and coherence.
Selecting appropriate diamond thickness and orientation for specific microcavity designs.
Designing metalization stacks for robust microwave pulse delivery and readout.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

Tech Support

Original Source

DOI: https://doi.org/10.1038/srep19482