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6CCVD Research

Improved entanglement detection with subspace witnesses

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-01-13
JournalPhysical review. A/Physical review, A
AuthorsWon Kyu Calvin Sun, A. R. COOPER, Paola Cappellaro
InstitutionsUniversity of Waterloo, Massachusetts Institute of Technology
Citations11
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”
  • Innovation: Introduction of the “subspace witness” (Ws), a robust metric for detecting entanglement that minimizes the impact of local unitary errors during State Preparation and Measurement (SPAM).
  • Robustness: Ws is achieved by maximizing the state fidelity measurement over a relevant entangled-state subspace (e.g., the Bell state phase φ), making detection insensitive to unknown phase shifts.
  • Performance Improvement: In a two-qubit solid-state system (NV center in diamond), Ws achieved a violation of -0.1827(4), significantly stricter than the standard state witness (Wψ) violation of -0.07421(4).
  • Efficiency: Ws requires fewer measurements than full Quantum State Tomography (QST). For n-qubit GHZ states, Ws requires only 3 measurements, making it highly efficient for large systems.
  • Quantification: Ws identifies the true (maximum) many-body coherences, facilitating improved lower bounds for entanglement quantification metrics, such as generalized concurrences.
  • System: The technique was experimentally validated using a hybrid two-qubit system composed of electronic spins in diamond, utilizing Hartmann-Hahn Cross-Polarization (HHCP) for gate operations.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Quantum System TypeHybrid Two-QubitN/ANV center electronic spin and nearby dark electronic spin-1/2 defect in diamond.
State Witness Violation (Wψ)-0.07421(4)N/AStandard fidelity measurement result.
Subspace Witness Violation (Ws)-0.1827(4)N/AOptimized fidelity measurement result, demonstrating improved detection.
Double-Quantum Coherence Time (T2)31(3)µsMeasured characteristic decay time under spin echo.
Entanglement Detection Threshold (τ*)33(3)µsTime limit until entanglement is no longer witnessed by Ws.
Two-Body Correlator Decay Time (T)25µsCharacteristic decay time fitted to exponentially decaying oscillations.
GHZ Subspace Dimension (d)2N/AConstant dimension for n-qubit GHZ states.
Ws Measurements for GHZ3N/ARequired measurements to extract Ws for any n-qubit GHZ state.
Entangling Gate MechanismHHCPN/AHartmann-Hahn Cross-Polarization sequence.

Key Methodologies

Section titled “Key Methodologies”
  1. Qubit Initialization: The system is initialized from thermal equilibrium using a Maxwell demon-type cooling scheme. This involves using spin non-conserving optical transitions under laser illumination to prepare the NV spin, followed by a SWAP operation (via HHCP) to transfer the state to the dark electronic spin.
  2. Entanglement Generation (U): The entangling gate (e.g., √iSWAP) is realized using the Hartmann-Hahn Cross-Polarization (HHCP) scheme, which exploits the intrinsic spin-spin coupling (Hint = dσz1σz2/2) by driving both spins with tuned microwave pulses.
  3. State Witness Measurement (Wψ): The standard state witness is measured by reconstructing the Bell state fidelity (Fψ). This requires measuring three two-body correlators (σx1σx2, σy1σy2, σz1σz2) using a sequence involving single-quubit rotations and free evolution under the coupling Hamiltonian.
  4. Subspace Witness Measurement (Ws): Ws is obtained by performing multiple fidelity measurements (e.g., at control phases φ = {0, π/2, π}) to fully identify the magnitude of the double-quantum coherence (pkk) and the population (P), allowing maximization of Fψ over the Bell subspace.
  5. Coherence Time Determination: The entanglement coherence time (τ*) is measured by applying the Ws measurement protocol after varying free evolution times (τ) under a spin echo sequence, tracking the phase-modulated decay of the coherence term C(φ).

Commercial Applications

Section titled “Commercial Applications”

The robust characterization methods developed using subspace witnesses are critical for validating and optimizing quantum hardware, particularly in diamond-based systems.

  • NISQ Quantum Computing:

    • Benchmarking: Provides an efficient and robust method for characterizing the quality of specific Genuine Multipartite Entangled (GME) states (GHZ, W, Dicke) generated in noisy, intermediate-scale quantum (NISQ) processors.
    • Gate Fidelity: Helps isolate the quality of the generated entanglement from local control errors (SPAM), enabling better assessment of two-qubit and multi-qubit gate performance.

  • Quantum Sensing and Metrology:

    • Enhanced Sensitivity: Applications like classical field sensing using GHZ states rely strictly on the magnitude of the many-body coherence. Ws accurately measures this maximum coherence, ensuring the generated state meets the requirements for entanglement-enhanced sensitivity.
    • Diamond Sensors: Directly applicable to improving the performance validation of NV-center based quantum sensors, which are used for high-resolution magnetic and electric field sensing.

  • Quantum Memory and Storage:

    • Decoherence-Free Subspaces: Ws can be used to characterize states (like W-states) used in decoherence-protected quantum memories, where the lifetime of stored quantum information depends on the coherence magnitude.

  • Solid-State Material Validation (Relevant to 6ccvd.com):

    • Diamond Quality Control: The NV center system relies on high-quality diamond substrates. Robust entanglement characterization serves as a sensitive metric for the quality and purity of the host diamond material, ensuring optimal spin properties and minimal environmental noise for quantum applications.
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”
  1. 2016 - International Conference on Micro- and Nano-Electronics 2016
  2. 2019 - International Conference on Micro- and Nano-Electronics 2018

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