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6CCVD Research

Deterministic preparation of W states via spin-photon interactions

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2021-05-18
JournalPhysical review. A/Physical review, A
AuthorsFatih Özaydin, Can Yesilyurt, Sinan Bugu, Masato Koashi
InstitutionsIstanbul University, Tokyo International University
Citations29
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research proposes a deterministic and efficient methodology for preparing arbitrary size W states (a class of robust multipartite entangled states) using spin-photon interactions, primarily focusing on Nitrogen Vacancy (NV) centers in diamond.

  • Deterministic W State Generation: The method achieves deterministic expansion of W states (Wn to Wn+1 or W2n), overcoming the inherent probabilistic nature of previous fusion-based schemes.
  • Optimized Three-Qubit Operation (O): A fundamental three-qubit operation is introduced, decomposed into only four Controlled-Z (CZ) gates and eight single-qubit gates (Hadamard and T’ gates).
  • Indirect Entanglement: The operation enables entanglement between two logical qubits (spins or photons) without requiring any direct interaction between them, relying instead on a single ancillary qubit (spin or photon) as a mediator.
  • Physical Platform: The scheme is designed for solid-state systems exhibiting spin-selective reflectivity, such as NV centers in diamond or quantum dots coupled to optical microcavities.
  • No Post-Selection Required: Crucially, the process requires neither post-measurement nor post-processing on the spin or photonic qubits, simplifying implementation in scalable quantum networks.
  • Robustness to Imperfections: Fidelity analysis shows that the fidelity of the generated W state is independent of the number of qubits (n), indicating robustness against gate imperfections during large-scale expansion.

Technical Specifications

Section titled “Technical Specifications”

The following parameters relate to the physical model (NV center coupled to an optical cavity) and the gate implementation requirements.

ParameterValueUnitContext
CZ Gate Conditiong > 5√κγDimensionlessRequired strong coupling regime for near-unity reflection phase shift (φ0 = π)
Resonant Conditionωp = ωc = ω0FrequencyIncident photon (ωp), cavity field (ωc), and electronic transition (ω0) frequencies must be matched
Ideal T’ Gate Angleθ = π/8RadiansRotation angle for the T’ single-qubit gate
Ideal Hadamard Angleθ = π/4RadiansRotation angle for the Hadamard (H) gate
Fidelity (Combined Imperfections)> 0.97DimensionlessAchieved fidelity when all gate imperfections (α, β, γ) are set to π/60
Ancillary Spin State (NV)+) orR>
Spin Coherence TimeHigh (e.g., > 10 ms)TimeNV centers in diamond are noted for high coherence times, even at room temperature
Controlled-Phase Gate (CP)Exp[i(π - γ)]N/APhase applied to the

Note: g is the coupling strength, κ is the cavity decay rate, and γ is the NV center decay rate.

Key Methodologies

Section titled “Key Methodologies”

The deterministic W state preparation relies on a modular, three-qubit expansion operation (O) implemented via spin-photon interactions.

  1. Three-Qubit Operation (O) Circuit Design:

    • The operation O acts on three inputs: Qubit 1 (W state component), Qubit 2 (new qubit, initially |0>), and Ancillary Qubit (Anc, mediator).
    • The circuit is decomposed into four Controlled-Z (CZ) gates (CZ1, CZ2, CZ3, CZ4) and eight single-qubit gates (six Hadamard, two T’).
    • The CZ gates are applied between Qubit 1 and Anc, and Qubit 2 and Anc, ensuring no direct interaction between the logical qubits (Qubit 1 and Qubit 2).

  2. Spin-Photon Interaction for CZ Gate:

    • The physical realization uses an NV center spin coupled to an optical cavity, leveraging spin-selective reflectivity.
    • An incident photon (e.g., |L> polarized) interacts with the NV spin, acquiring a phase shift (eiφ) dependent on the spin state (|-> or |+>).
    • Under resonant conditions (ωp = ωc = ω0) and strong coupling (g > 5√κγ), this interaction realizes a near-ideal CZ gate between the photon polarization and the NV spin state.

  3. W State Expansion Strategy (Doubling):

    • Initial State: Start with a separable state (e.g., |1>|0>|0> for Bell pair creation) or an existing Wn state.
    • Expansion Step: Apply the operation O to one qubit from the existing Wn state (Input 1), a new qubit in |0> (Input 2), and the ancillary mediator. This creates a W-like state with one additional qubit.
    • Doubling: By repeating this expansion process for every qubit in the initial Wn state, the size of the W state is doubled (Wn → W2n).

  4. Implementation Platforms:

    • Photonic W States: Use an NV center spin as the ancillary mediator to entangle two non-interacting, circularly polarized photons.
    • Spin W States (Distant NV Centers): Use a single ancillary photon (e.g., |R>) to mediate entanglement between two spatially separated NV center spins (NV1 and NV2).

  5. Fidelity Analysis:

    • Non-ideal gates (H(α), T’(β), CP(γ)) are modeled using rotation angles (α, β) and phase error (γ).
    • The calculated fidelity (FCombined) is found to be independent of the number of qubits (n), confirming the scalability and robustness of the expansion protocol against local gate errors.

Commercial Applications

Section titled “Commercial Applications”

The deterministic generation of robust multipartite entangled states (W states) using solid-state systems like NV centers has direct implications for next-generation quantum technologies.

Industry/FieldApplication/ProductRelevance to Technology
Distributed Quantum ComputingQuantum Network Nodes, Quantum ProcessorsNV centers serve as high-coherence, solid-state qubits ideal for network nodes; deterministic entanglement is essential for linking these nodes.
Quantum CommunicationQuantum Repeaters, Secure CommunicationW states are robust against qubit loss, making them superior resources for maintaining entanglement across long-distance quantum communication channels.
Solid-State Quantum HardwareScalable Quantum Chips (Diamond/SiC)The scheme utilizes established solid-state platforms (NV centers, SiV centers, quantum dots) compatible with current microcavity and nanofabrication techniques.
Quantum SimulationRobust Entanglement ResourcesW states are valuable for simulating complex physical systems due to their inherent robustness compared to GHZ states.
Quantum Metrology/SensingHigh-Precision SensorsWhile the paper focuses on entanglement, the underlying NV center technology is critical for high-sensitivity magnetometers and thermometers due to long coherence times.
View Original Abstract

Spin systems such as silicon or nitrogen vacancy centers in diamond, quantum\ndots and quantum dot molecules coupled to optical cavities appear as key\nelements for creating quantum networks as not only constituting the nodes of\nthe network, but also assisting the creation of photonic networks. Here we\nstudy deterministic preparation of arbitrary size $W$ states with spin systems.\nWe present an efficient operation on three qubits, two being the logical qubits\nand one being the ancillary qubit, where no interaction between the logical\nqubits are required. The proposed operation can create a $W$-type\nEinstein-Podolsky-Rosen (EPR) pair from two separable qubits, and expand that\nEPR pair or an arbitrary size $W$ state by one, creating a $W$-like state.\nTaking this operation as the fundamental building block, we show how to create\na large scale $W$ state out of separable qubits, or double the size of a $W$\nstate. Based on this operation and focusing on nitrogen vacancy (NV) centers in\ndiamond as an exemplary spin system, we propose a setup for preparing $W$\nstates of circularly polarized photons, assisted by a single spin qubit, where\nno photon-photon interactions are required. Next, we propose a setup for\npreparing $W$ states of spin qubits of spatially separated systems, assisted by\na single photon. We also analyze the effects of possible imperfections in\nimplementing the gates on the fidelity of the generated $W$ states. In our\nsetups, neither post-measurement, nor post-processing on the states of spin or\nphotonic qubit is required. Our setups can be implemented with current\ntechnology, and we anticipate that they contribute to quantum science and\ntechnologies.\n

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1989 - Bell’s Theorem, Quantum Theory, and Conceptions of the Universe
  2. 2000 - Quantum Computation and Quantum Information

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