Orbital and electronic entanglement in quantum teleportation schemes
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-08-06 |
| Journal | Physical Review Research |
| Authors | Anna Galler, Patrik Thunström, Anna Galler, Patrik Thunström |
| Institutions | Uppsala University, Ăcole Polytechnique |
| Citations | 6 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research investigates the fundamental role of electronic entanglementâspecifically mode entanglement (orbital correlation) and particle entanglement (Slater determinant distance)âas resources for solid-state quantum teleportation schemes.
- Core Distinction: The study confirms that mode entanglement and particle entanglement are distinct resources for identical particles (electrons), unlike the single definition used for distinguishable particles.
- Resource Requirement: Particle entanglement is shown to be crucial for achieving a 100% success rate in quantum teleportation protocols, typically requiring the use of maximally entangled Bell states.
- Protocol Validation: Three distinct solid-state electronic teleportation schemes were proposed and analyzed: a hydrogen molecule (H2) on graphene, a neutral Nitrogen-Vacancy (NV0) center in diamond, and a linear quantum dot (QD) array.
- Performance Trade-off: The H2/graphene scheme, which relies only on mode entanglement and avoids creating particle entanglement within the system, is limited to a 50% success rate.
- High-Fidelity Schemes: Both the NV0 center and the QD array schemes achieved a theoretical 100% success rate by utilizing initial resource states that are maximally particle and mode entangled.
- Material Science Insight: The analysis highlights that particle interactions (like Coulomb interaction) are necessary to generate particle entanglement, while non-local one-particle potentials generate mode entanglement.
Technical Specifications
Section titled âTechnical SpecificationsâThe following metrics and operational constraints were derived from the analysis of the proposed ideal quantum teleportation schemes.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| H2 Adsorption Energy | ~0.4 | eV | Binding energy of H2 to a graphene vacancy site |
| H2 Teleportation Success Rate | 50 | % | Limited by particle number superselection rules (N-SSR) |
| NV0/QD Teleportation Success Rate | 100 | % | Achieved using maximally entangled Bell states |
| NV0 Initial Particle Entanglement (EG) | 1/2 | Dimensionless | Geometric measure for the two-hole resource state |
| NV0 Initial Particle Entanglement (S) | 1 | Dimensionless | Entropic measure for the two-hole resource state |
| Required Phase Shift Time (H2) | pi/(”B) | Time | Magnetic field pulse duration for Bobâs correction operation |
| QD Conditional Tunneling Time | pi/U | Time | Time required for W(2) evolution (U is the effective Coulomb interaction) |
| Particle Entanglement Inequality | E[PD | Κ2>] >= αE[ | Κe>] + (1 - α)E[ |
Key Methodologies
Section titled âKey MethodologiesâThe study employed theoretical analysis using the second quantization formalism to model electron states and their evolution under specific Hamiltonians, focusing on three distinct solid-state platforms.
1. H2 Molecule on Graphene (STM-Assisted)
Section titled â1. H2 Molecule on Graphene (STM-Assisted)â- Setup: H2 molecule adsorbed on a single graphene vacancy site, addressable by a spin-polarized Scanning Tunneling Microscope (STM) tip.
- Resource State: H2+ ion (one electron) in its binding orbital, shared between atoms A (Alice) and B (Bob). This state is mode entangled but not particle entangled.
- State Injection: A second electron (the state to be teleported) is injected via the STM tip into a superposition of the binding and anti-binding orbitals.
- Measurement: Alice performs a magnetization measurement (spin measurement along the y-axis) on the electrons localized at atom A.
- Correction: Bob applies a magnetic field pulse (duration t = pi/(”B)) to the electron spin on atom B to complete the transfer, achieving a 50% success rate.
2. Neutral NV0 Center in Diamond
Section titled â2. Neutral NV0 Center in Diamondâ- Setup: A neutral Nitrogen-Vacancy (NV0) center, involving five electrons (three holes) in eight spin-orbitals (N-p and C-p dangling bonds).
- Resource State: A maximally particle and mode entangled Bell state of two holes, residing in the N and C orbitals (S = 1, EG = 1/2).
- State Injection: The state to be teleported is encoded in the spin state of a third hole in the C, ml = 0 orbital.
- Measurement: Alice performs a Bell state measurement using spin-flip Coulomb interactions between the holes.
- Correction: Bob applies spin-flip operations based on Aliceâs measurement outcome, achieving a 100% success rate.
3. Quantum Dot (QD) Array
Section titled â3. Quantum Dot (QD) Arrayâ- Setup: A linear array of three semiconductor quantum dots (Dot 1, Dot 2, Dot 3). Dot 1 and 2 belong to Alice; Dot 3 belongs to Bob.
- Resource State Creation: Two electrons in Dot 3 are used to create a maximally particle and mode entangled singlet state between Dot 2 and Dot 3 via a conditional tunneling process (governed by the two-particle unitary operator W(2)).
- State Injection: The state to be teleported is encoded in the spin state of an electron in Dot 1.
- Coupling: A second conditional tunneling process is allowed between Dot 1 and Dot 2, coupling the state to be teleported with the entangled resource.
- Measurement/Correction: Alice performs a charge and/or magnetization measurement on Dot 1. Bob applies a unitary spin rotation on Dot 3 to recover the original state, achieving a 100% success rate.
Commercial Applications
Section titled âCommercial ApplicationsâThis fundamental research on electronic entanglement and teleportation directly supports the development and optimization of next-generation quantum hardware.
- Solid-State Quantum Computing: Provides theoretical blueprints for implementing quantum gates and reliable qubit transport mechanisms in electron-based solid-state architectures (e.g., silicon quantum dots, diamond NV centers).
- Qubit Interconnects: The teleportation schemes offer a method for transferring quantum information between distant qubits without requiring phase-coherent physical transport of the electron itself, crucial for scaling up quantum processors.
- Quantum Memory and Sensing: NV centers are leading candidates for robust quantum memories and sensors. Understanding entanglement dynamics in NV0 centers aids in designing high-fidelity spin-qubit operations.
- Strongly Correlated Materials Design: The distinction between mode and particle entanglement is essential for accurately modeling and engineering materials where electron-electron interactions (Coulomb terms) dominate, such as transition metal oxides used in advanced electronics.
- Quantum Cryptography: The principles demonstrated here are foundational for secure quantum communication protocols that rely on entanglement distribution using indistinguishable particles.
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.