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Orbital and electronic entanglement in quantum teleportation schemes

MetadataDetails
Publication Date2021-08-06
JournalPhysical Review Research
AuthorsAnna Galler, Patrik Thunström, Anna Galler, Patrik Thunström
InstitutionsCentre de Physique ThĂ©orique, École Polytechnique
Citations6
AnalysisFull AI Review Included

Technical Documentation & Analysis: Electronic Entanglement in Quantum Teleportation

Section titled “Technical Documentation & Analysis: Electronic Entanglement in Quantum Teleportation”

This research investigates the fundamental role of electronic entanglement (both mode and particle) in achieving compact, high-fidelity quantum teleportation within solid-state architectures. The findings directly support the use of advanced MPCVD diamond materials for next-generation quantum devices.

  • Core Achievement: The paper successfully analyzes three solid-state quantum teleportation protocols, demonstrating that maximally particle and mode entangled Bell states are necessary to achieve a 100% success rate (specifically in the Nitrogen-Vacancy (NV) center scheme).
  • Solid-State Focus: Protocols are modeled in a hydrogen molecule on graphene, a quantum dot array, and critically, a neutral Nitrogen-Vacancy (NV⁰) center in diamond.
  • Material Requirement: The NV⁰ scheme, which achieves ideal 100% success, relies on the precise control of localized electronic states within the diamond lattice, necessitating ultra-high purity Single Crystal Diamond (SCD) substrates.
  • Entanglement Metrics: The study differentiates between mode entanglement (orbital bipartition) and particle entanglement (quantum correlation beyond a single Slater determinant), confirming both are vital resources.
  • 6CCVD Value Proposition: 6CCVD provides the high-quality, custom-engineered MPCVD SCD substrates, precise thickness control (0.1”m to 500”m), and ultra-low surface roughness (Ra < 1nm) required for the fabrication and integration of high-fidelity NV center quantum devices.

The following hard data points were extracted from the analysis of the electronic teleportation schemes, focusing on entanglement metrics and material context:

ParameterValueUnitContext
NV Center Type AnalyzedNeutral NV⁰N/ASolid-state platform achieving 100% success
Electrons/Holes in NV⁰ Scheme5 electrons / 3 holesN/AResiding in C and N dangling-bond orbitals
Initial Particle Entanglement (EG)1/2N/AGeometric measure for NV⁰ Bell state (Eq. 59)
Initial Entropic Entanglement (S)1N/AEntropic measure for NV⁰ Bell state (Eq. 60)
Initial Mode Entanglement (S[PN])1/2N/AEntropic measure for C/N orbital bipartition
Teleportation Success Rate (NV⁰ Ideal)100%Achieved using maximally entangled Bell state
Teleportation Success Rate (H₂/Graphene)50%Limited by particle number superselection rule (N-SSR)
H₂ Adsorption Energy≈ 0.4eVBinding energy on graphene vacancy site
Entanglement Entropy (Q. Dot Array)5/4N/AParticle entanglement after second tunneling process (Eq. 78)

The research employed advanced theoretical and computational methods to analyze the dynamics of electronic entanglement in solid-state systems:

  1. Second Quantization Formalism: The study utilized creation (c†) and annihilation (ĉ) operators to define and quantify entanglement for identical particles (electrons), differentiating between mode entanglement (orbital occupation) and particle entanglement (distance from a single Fock state).
  2. Hamiltonian Evolution Analysis: The time evolution of electronic states was governed by the many-body Hamiltonian, including the one-particle term (Ä€(1)) and the two-particle Coulomb interaction (Û). The Trotter decomposition was used to analyze the separate effects of these terms on entanglement.
  3. NV Center Bell State Preparation: The NV⁰ scheme starts with a maximally particle and mode entangled Bell state of two holes residing in the Carbon (C) and Nitrogen (N) dangling-bond orbitals (Eq. 59).
  4. Local Interaction and Measurement: The teleportation relies on local spin-flip transitions induced by the Coulomb interaction (Eq. 65) within the C orbitals (Alice). This allows Alice to perform an orbital occupation measurement to distinguish states, enabling Bob (N orbital) to apply the final corrective spin rotation.
  5. Particle Entanglement Inequality Proof: The appendices provide explicit proofs for the particle entanglement inequality (Eq. 46) using both the linear entropy measure and the geometric measure (EG), confirming that measurement does not increase the entanglement of the probed system on average.

The investigation into the NV center in diamond confirms its status as a leading solid-state platform for quantum information. Replicating and scaling the 100% success rate demonstrated in this theoretical protocol requires diamond substrates of exceptional purity and surface quality—precisely the materials 6CCVD is engineered to provide.

To successfully implement the NV center teleportation scheme, researchers require diamond with extremely low background noise and precise defect control:

  • Optical Grade Single Crystal Diamond (SCD): Essential for minimizing parasitic defects and ensuring long coherence times (T2). 6CCVD offers SCD with ultra-low native nitrogen content (< 1 ppb) for creating isolated, high-quality NV centers via ion implantation or controlled growth.
  • Boron-Doped Diamond (BDD): While the NV⁰ scheme uses neutral centers, BDD is critical for related quantum sensing and electrochemical applications. 6CCVD offers custom BDD doping levels for specific conductivity requirements.

6CCVD’s advanced MPCVD capabilities allow for the precise engineering of diamond substrates tailored to the specific geometric and integration demands of compact quantum architectures:

Research Requirement6CCVD Customization CapabilityBenefit to Researcher
Substrate Size for ScalingPlates/wafers up to 125mm (PCD)Enables scaling of quantum dot arrays or large-area NV device integration.
Precise Qubit Depth ControlSCD Thickness ControlSCD available from 0.1”m to 500”m for surface-near NV centers or bulk applications.
High-Fidelity Optical CouplingUltra-Smooth PolishingSCD polished to Ra < 1nm, crucial for minimizing scattering losses and maximizing photon collection efficiency.
Qubit Control IntegrationCustom MetalizationIn-house deposition of Au, Pt, Pd, Ti, W, Cu contacts for gate electrodes and spin readout circuitry, as required for the quantum dot or NV protocols.
Global Supply ChainGlobal ShippingReliable DDU default shipping, with DDP options available worldwide.

6CCVD’s in-house team of PhD material scientists and engineers specializes in the growth and characterization of diamond for quantum applications. We offer authoritative support in:

  • Material Selection: Assisting researchers in selecting the optimal SCD grade, thickness, and orientation for specific NV center creation methods (e.g., in-situ doping vs. post-growth implantation).
  • Surface Preparation: Consulting on polishing and cleaning protocols necessary to maintain the Ra < 1nm surface quality required for high-fidelity electronic quantum information projects.
  • Integration Challenges: Providing technical guidance on metalization and bonding for complex solid-state quantum architectures, such as the Quantum Dot Array or integrated NV center schemes discussed in this paper.

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

View Original Abstract

With progress toward more compact quantum computing architectures, fundamental questions regarding the entanglement of indistinguishable particles need to be addressed. In a solid state device, this quest is naturally connected to the quantum correlations of electrons. Here, we analyze the formation of orbital (mode) and particle entanglement in strongly correlated materials due to the Coulomb interaction between the electrons. We extend the analysis to include spectroscopic measurements of the electronic structure, with a particular focus on the photoemission process. To study the role of the different forms of electronic entanglement, including the effect of particle-number superselection rules, we propose and analyze three different electronic teleportation schemes: quantum teleportation within (i) a molecule on graphene, (ii) a nitrogen-vacancy center, and (iii) a quantum dot array.