Qubit-environment negativity versus fidelity of conditional environmental states for a nitrogen-vacancy-center spin qubit interacting with a nuclear environment

At a Glance

Metadata	Details
Publication Date	2020-10-08
Journal	Physical review. A/Physical review, A
Authors	Małgorzata Strzałka, Damian Kwiatkowski, Łukasz Cywiński, Katarzyna Roszak
Institutions	Wrocław University of Science and Technology, Polish Academy of Sciences
Citations	11
Analysis	Full AI Review Included

Technical Documentation & Analysis: NV-Center Qubit Entanglement in MPCVD Diamond

This document analyzes the research paper “Qubit-environment Negativity versus Fidelity of conditional environmental states for an NV-center spin qubit interacting with a nuclear environment” to provide technical specifications and highlight how 6CCVD’s advanced MPCVD diamond materials and customization capabilities directly enable and extend this critical quantum computing research.

Executive Summary

The research investigates the fundamental relationship between qubit-environment entanglement (quantified by Negativity, N) and the difference in conditional environmental states (quantified by 1 - Fidelity, 1 - F) within a solid-state quantum system.

Core System: The study models the Nitrogen-Vacancy (NV) center in diamond as an electronic spin S=1 qutrit, utilizing two-level subspaces as the qubit.
Environment: The decoherence environment is modeled as a sparse bath of partially polarized ¹³C nuclear spins, which are intrinsic to the diamond lattice.
Key Finding: A remarkable agreement is found between the time evolution of Negativity (N) and the one-minus-Fidelity (1 - F), suggesting that the amount of entanglement generated is proportional to the “trace” the joint evolution leaves on the environment.
Methodological Significance: This correlation provides a physically intuitive and computationally feasible measure for quantifying entanglement in large, mixed-state bipartite systems undergoing pure dephasing.
Parameter Dependence: Entanglement generation is observed across various Hamiltonian variants and magnetic fields (B_z = 0 T and 0.2 T), provided the nuclear environment is partially or fully polarized (p > 0).
Material Requirement: Successful experimental realization of this work relies critically on high-purity Single Crystal Diamond (SCD) with precise control over the ¹³C isotopic concentration to define the nuclear spin bath.

Technical Specifications

The following hard data points were extracted from the analysis of the NV-center spin qubit system and its environment.

Parameter	Value	Unit	Context
Zero-Field Splitting (Δ)	2.87	GHz	NV center S=1 qutrit system
Electron Gyromagnetic Ratio (γ_e)	28.08	MHz/T	Used in free qutrit evolution Hamiltonian
¹³C Nuclear Gyromagnetic Ratio (γ_n)	10.71	MHz/T	Used in free environmental spin evolution
Applied Magnetic Field (B_z) Tested	0, 0.2	T	Field applied along the NV center’s z-axis
Environmental Spin Count	5	N/A	Randomly chosen ¹³C isotopes (spin 1/2)
Initial Nuclear Polarization (p) Range	0.1 to 1	N/A	Tested range for the mixed environmental state
Qubit Subspaces Studied	m=0, 1 and m=-1, 1	N/A	Two distinct qubit definitions within the S=1 qutrit
Maximum Evolution Time	15	µs	Time scale for observing entanglement dynamics

Key Methodologies

The theoretical framework relies on precise modeling of the solid-state environment and advanced quantum information metrics.

System Initialization: The qubit is initialized in a pure superposition state (e.g., a|0> + b|1>), while the nuclear environment is initialized in a partially polarized mixed state, R(0).
Hamiltonian Construction: The total system Hamiltonian (Ĥ) includes the free evolution of the qutrit, the free evolution of the environmental ¹³C spins (Ĥ_E), and the hyperfine interaction (V) between the electronic spin and the nuclear spins.
Time Evolution Calculation: The time-evolved qubit-environment density matrix, ρ(t), is calculated using the evolution operator Û(t), which incorporates the environmental operators ŵ_m(t) conditional on the qubit pointer states.
Entanglement Quantification (Negativity): Negativity, N(ρ), is calculated by performing a partial transposition (Γ) on the joint density matrix ρ(t) and summing the absolute values of the negative eigenvalues (λ_i < 0).
Conditional State Comparison (Fidelity): The difference between the conditional environmental states (R_nn(t) and R₁₁(t)) is quantified using the Fidelity measure: 1 - F(R_nn, R₁₁).
Correlation Analysis: The time evolution of N(t) is directly compared against 1 - F(t) across variations in magnetic field and initial environmental polarization (p) to establish the conjectured proportionality.

6CCVD Solutions & Capabilities

This research confirms the critical role of the diamond host material in solid-state quantum computing. 6CCVD provides the necessary high-purity, customizable MPCVD diamond substrates required to replicate, extend, and scale this fundamental NV-center research into functional quantum devices.

Research Requirement	6CCVD Material Solution	Technical Specification & Advantage
High Coherence Host Material	Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen and defect concentration, maximizing the intrinsic T₂ coherence time of the NV centers.
Controlled Nuclear Spin Bath	Isotopically Engineered SCD Wafers	We supply SCD with precise control over ¹³C concentration. Researchers can choose Highly Depleted ¹³C (< 0.1%) for maximum isolation (T₂ extension) or Enriched ¹³C (up to 99%) for controlled, dense spin bath interaction studies, directly enabling the modeling presented.
Substrate Dimensions	Custom Dimensions & Thickness	SCD plates available in thicknesses from 0.1µm up to 500µm. We offer custom plates and wafers up to 125mm (PCD), suitable for large-scale experimental integration.
Surface Quality for Qubit Control	Precision Polishing (Ra < 1nm)	SCD wafers are polished to an atomic-scale roughness (Ra < 1nm). This is crucial for minimizing surface-related decoherence and ensuring high-fidelity coupling for optical and microwave control.
Integration of Control Lines	Custom Metalization Services	We provide in-house deposition of critical metals (Au, Pt, Pd, Ti, W, Cu). This allows engineers to pattern microwave striplines or magnetic field coils directly onto the diamond surface for precise control of B_z and qubit transitions.
Boron Doping for Electrodes	Boron-Doped Diamond (BDD)	For applications requiring conductive diamond electrodes or integrated sensors, we offer highly conductive BDD films (PCD or SCD).

Engineering Support

6CCVD’s in-house team of PhD material scientists specializes in optimizing MPCVD growth parameters to meet the stringent requirements of quantum applications. We offer comprehensive consultation on material selection, isotopic control, and surface preparation necessary for similar NV-center spin qubit projects.

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

View Original Abstract

We study the evolution of qubit-environment entanglement, quantified using Negativity, for NV-center spin qubits interacting with an environment of $^{13}$C isotope partially polarized nuclear spins in the diamond lattice. We compare it with the evolution of the Fidelity of environmental states conditional on the pointer states of the qubit, which can serve as a tool to distinguish between entangling and non-entangling decoherence in pure-dephasing scenarios. The two quantities show remarkable agreement during the evolution in a wide range of system parameters, leading to the conclusion that the amount of entanglement generated between the qubit and the environment is proportional to the trace that the joint evolution leaves in the environment.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.102.042602

References

2003 - Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing