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6CCVD Research

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

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-10-08
JournalPhysical review. A/Physical review, A
AuthorsMaƂgorzata StrzaƂka, Damian Kwiatkowski, Ɓukasz CywiƄski, Katarzyna Roszak
InstitutionsPolish Academy of Sciences, WrocƂaw University of Science and Technology
Citations11
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research investigates the relationship between quantum entanglement generation and the resulting trace left on the environment during pure-dephasing evolution of a Nitrogen-Vacancy (NV) center spin qubit in diamond.

  • Core Finding: The amount of qubit-environment entanglement, quantified by Negativity (N), is found to be highly proportional to the difference between the conditional environmental states, quantified by (1 - Fidelity).
  • Methodological Simplification: This correlation suggests that entanglement in mixed-state, pure-dephasing scenarios can be quantified by measuring the “trace” the joint evolution leaves on the environment, offering a simpler alternative to calculating Negativity.
  • System Model: The study uses a realistic model of an NV-center spin qubit (S=1 qutrit, utilizing two levels) interacting with a sparse bath of partially polarized 13C nuclear spins.
  • Robustness: The agreement between Negativity and (1 - Fidelity) was observed across a wide range of system parameters, including different qubit choices (m=0,1 vs m=-1,1), zero and non-zero magnetic fields (Bz=0 and Bz=0.2 T), and varying initial nuclear polarization (p=0.1 to p=1).
  • Physical Interpretation: The results support the conjecture that the degree of entanglement generated is proportional to how different the two environmental states (conditional on the qubit pointer states) become during the evolution.
  • Implication for Detection: This work moves beyond merely detecting the presence of entanglement to quantifying its magnitude using a measure derived from environmental state differences.

Technical Specifications

Section titled “Technical Specifications”

The following parameters define the physical system and the simulation conditions used for the NV-center spin qubit and its 13C nuclear environment.

ParameterValueUnitContext
NV Center Electronic SpinS = 1DimensionlessEffective qutrit system
Zero-Field Splitting (Δ)2.87GHzEnergy gap between spin states
Electron Gyromagnetic Ratio (Îłe)28.08MHz/TNV Center
13C Nuclear Gyromagnetic Ratio (Îłn)10.71MHz/TEnvironmental spins
Simulated Environment Size (N)5NucleiRandomly located 13C isotopes
Applied Magnetic Field (Bz)0 and 0.2TTested conditions
Initial Nuclear Polarization (p)0.1 to 1DimensionlessPolarization of the 13C bath
Qubit Subspaces Testedm=0, 1 and m=-1, 1Spin StatesTwo different two-level qubit definitions
Interaction TypeHyperfine (Dipolar)Hamiltonian TermQubit-environment coupling

Key Methodologies

Section titled “Key Methodologies”

The study utilized numerical simulation and theoretical modeling based on the NV-center Hamiltonian to track the joint qubit-environment density matrix evolution.

  1. System Definition: The system consists of an NV-center electronic spin (S=1) coupled to a sparse environment of N=5 13C nuclear spins (spin 1/2).
  2. Hamiltonian Formulation: The total Hamiltonian (H) includes the free evolution of the qutrit, the free evolution of the nuclear environment (HE), and the hyperfine interaction (V), which is restricted to the pure dephasing type (commutes with system pointer states).
  3. Initial State Preparation: The initial state is a product state: a pure superposition state of the qubit (e.g., a|0> + b|1>) and a partially polarized (mixed) state of the nuclear environment R(0), where the polarization (p) is varied from 0.1 (highly mixed) to 1 (fully polarized).
  4. Evolution Operator Calculation: The time evolution operator U(t) is calculated, leading to the time-evolved joint density matrix ρ(t).
  5. Entanglement Quantification (Negativity): Negativity N(ρ) is calculated by performing a partial transposition of ρ(t) with respect to the qubit and summing the absolute values of the negative eigenvalues.
  6. Environmental Trace Quantification (Fidelity): The conditional environmental states Rii(t) (the state of the environment if the qubit were found in pointer state i) are calculated. The difference between these states is quantified using the Fidelity measure: F(Rnn, R11). The metric used for comparison is (1 - Fidelity).
  7. Comparison and Correlation: The time evolution of N(t) is compared directly against the time evolution of 1 - F(t) across various magnetic field and polarization conditions to establish proportionality.

Commercial Applications

Section titled “Commercial Applications”

The findings directly support the engineering and optimization of quantum devices based on solid-state spin systems, particularly those utilizing NV centers in diamond.

  • Quantum Computing and Memory:
    • Provides a robust, physically intuitive metric (1 - Fidelity) for quantifying entanglement buildup in mixed-state quantum systems, which is essential for validating quantum gate operations and characterizing quantum memory performance.
    • Aids in designing control sequences (like dynamical decoupling) that minimize unwanted entanglement with the environment while preserving qubit coherence.
  • Quantum Sensing and Metrology:
    • NV centers are leading candidates for nanoscale magnetic and electric field sensing. Understanding the entanglement dynamics helps optimize the coherence time (T2) and sensitivity of these sensors, especially in environments where nuclear polarization is utilized.
  • Dynamic Nuclear Polarization (DNP):
    • The study relies on the preparation of partially polarized nuclear spins (p > 0), a technique often achieved via NV centers to hyperpolarize 13C nuclei. This is critical for enhancing signals in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI).
  • Solid-State Qubit Engineering:
    • The methodology is applicable to other solid-state qubits (e.g., quantum dots, silicon carbide defects) that operate under pure dephasing conditions, allowing engineers to better diagnose and mitigate decoherence sources.
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

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2003 - Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing

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