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Qubit teleportation between non-neighboring nodes in a quantum network
S. L. N. Hermans, M. Pompili, H. K. C. Beukers, S. Baier, J. Borregaard, R. Hanson
TL;DR
The paper realizes unconditional qubit teleportation between non-neighboring nodes using a three-node quantum network. Its readout, memory-protection, and heralding innovations support future multi-node protocols and applications.
Problem
The work addresses qubit teleportation between non-neighboring nodes in a quantum network, a capability relevant to exploring more complex protocols.
Method
A three-node network establishes two remote entangled links, performs entanglement swapping at the middle node, and uses protected memory-qubit readout and tailored heralding.
Results
The experiment realizes unconditional qubit teleportation between non-neighboring nodes in a quantum network.
Takeaways & Limitations
The demonstrated methods provide a building block for future quantum networks and can be transferred to several other solid-state qubit platforms.
Takeaways & Limitations
An improved optical interface is expected to increase both the teleportation protocol rate and fidelity.
Abstract
from arXiv · showhide
Future quantum internet applications will derive their power from the ability to share quantum information across the network. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections. While many experimental demonstrations have been performed on different quantum network platforms, moving beyond directly connected nodes has so far been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighboring nodes in a quantum network. The network employs three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications.
Outlook
The experiment realizes unconditional qubit teleportation between non-neighboring nodes using a three-node network, memory qubits, entanglement swapping, and feed-forward. The reported innovations improve readout, memory protection, and rejection of false heralding signals, supporting future multi-node protocols.
- Outlook: The work realizes unconditional teleportation between non-neighboring nodes and introduces methods intended to support more complex protocols and transfer to other solid-state platforms.The cited platforms include group-IV color centers, SiC vacancy-related qubits, and single rare-earth ions.
- Outlook: The experiment teleports a qubit from Charlie to Alice, which are non-neighboring nodes in a three-node Alice–Bob–Charlie network.Each node contains a diamond NV center; Bob and Charlie additionally use nearby ^13C nuclear spins as memory qubits.
- Outlook: Bob stores his share of the Alice–Bob entangled state in a memory qubit before generating entanglement on the Bob–Charlie link.Each entanglement attempt can decohere Bob’s memory, so the second-link generation is bounded by a timeout.
- Outlook: Bob performs a Bell-state measurement to swap entanglement between Alice and Charlie, after which Charlie applies feed-forward and stores his state in memory.The required operation depends on Bob’s measurement outcomes and the detectors heralding the individual links.
- Outlook: Charlie prepares the input qubit, performs a Bell-state measurement, and sends its outcomes to Alice for the final feed-forward operation.Alice verifies the teleported state by measuring in corresponding positive and negative basis directions to reduce tomography bias.
II. EXPERIMENTAL SETUP
The setup adds a ^13C nuclear-spin memory at Charlie and a classical channel allowing Charlie to send Bell-state measurement results directly to Alice.
- II. EXPERIMENTAL SETUP: Charlie uses a carbon-13 nuclear spin as a memory qubit.The experiment also establishes a classical communication channel from Charlie to Alice for transmitting Bell-state measurement results.
III. TAILORED HERALDING OF THE REMOTE ENTANGLED STATES
The tailored heralding scheme uses local PSB detections to identify false entanglement heralds caused by extra photon emissions. Measurements distinguish double optical excitation from double |0⟩ occupancy and quantify these error sources.
- III. TAILORED HERALDING OF THE REMOTE ENTANGLED STATES: Double |0⟩ occupancy and double optical excitation emit an extra photon that local PSB detectors can use to reject false heralding in real time.The scheme monitors PSB detectors during and after optical excitation.
- III. TAILORED HERALDING OF THE REMOTE ENTANGLED STATES: PSB photons detected during the optical pulse primarily flag double excitation errors, whereas post-pulse detections are associated with double |0⟩ occupancy.The computational-basis outcome patterns differ between the two detection-time regimes.
- III. TAILORED HERALDING OF THE REMOTE ENTANGLED STATES: The extracted double |0⟩ occupancy probabilities correspond to αAlice = 0.07, αBob = 0.05, and αCharlie = 0.10.The estimates are obtained by correcting PSB detection data for detection efficiency under stated assumptions about dark counts and error-source dominance.
A. Numerical model
The numerical model represents NV-center excitation, spontaneous and double emission, photon-mode branching, transmission loss, and undetected modes to predict the communication-qubit and photon state used in entanglement analysis.
- A. Numerical model: The model treats each NV center as a three-level system with ground states |0⟩, |1⟩, and excited state |e⟩ driven on the resonant |0⟩↔|e⟩ transition.The dynamics are described by a rotating-frame Hamiltonian with time-dependent optical driving Ω(t).
- A. Numerical model: Spontaneous emission is modeled with a Lindblad operator, while a second jump operator captures double-emission processes.The master equation is solved in a basis containing zero-, one-, and two-photon states.
- A. Numerical model: The simulation calculates probabilities P0, P1, and P2 for emitting zero, one, or two photons, with P0 + P1 + P2 = 1.Emission of more than two photons is neglected.
- A. Numerical model: Photons are partitioned into PSB and ZPL modes using Pz = 3%, and detection windows distinguish photons accepted by the PSB and ZPL detectors.The emitted photon transformation is modeled as a beam-splitter transformation between ZPL and PSB modes.
- A. Numerical model: Transmission and detection efficiencies are included through ηz for the NV-to-beam-splitter path and ηb for PSB transmission and detection.The model traces over lost or undetected modes and represents the remaining state with unnormalized density matrices ρ0, ρ1, and ρ2.
- A. Numerical model: The model incorporates node-dependent parameters, phase differences, detector assumptions, and reduced coherence from imperfect ZPL-photon visibility.It neglects dark counts and allows parameters such as α, Ω, and transmission efficiencies to differ between centers.
IV. MEMORY QUBIT COHERENCE BOB
The memory-qubit decoupling sequence is evaluated through cardinal-state storage and superposition-state decay. Applying πM substantially improves memory coherence and initial state quality.
- Memory-qubit coherence: The experiment characterizes memory coherence by storing six cardinal states and comparing decoupling with no-pulse and idle controls.Eigenstate and superposition-state fidelities are averaged separately.
- Memory-qubit coherence: Eigenstates show little decay over the measured range, while superposition-state decay is fitted as a function of entanglement-attempt number.The fitted parameters are reported in Table IV.
- Decoupling benefit: More than 6×: the πM decoupling pulse increases N1/e for the memory qubit.The pulse also produces a higher initial Bloch-vector length A.
- Decoupling benefit: The higher initial Bloch-vector length is mainly explained by phase stabilization between swapping the state onto the memory qubit and beginning entanglement generation.The stabilization lasts approximately 350 µs, during which intrinsic T2* dephasing affects the memory unless πM is applied.
V. COMMUNICATION QUBIT COHERENCE
Communication-qubit decoupling is applied at protocol-specific times to preserve coherence during entanglement generation and teleportation. The resulting state fidelities are characterized across different decoupling durations.
- Decoupling protocol: Communication qubits are decoupled at node-specific protocol stages, including after link heralding and during memory-qubit re-phasing.On Alice, decoupling continues until Charlie sends the Bell-state-measurement result.
- Fidelity characterization: State fidelities are measured for different decoupling times and fitted with f(t) = Ae^−(t/τcoh)^n + 0.5.Eigenstates and superposition states are investigated separately, with timing bounds set by successful attempts and the 1000-attempt timeout.
VI. BASIS-ALTERNATING REPETITIVE READOUT
Charlie’s memory-qubit readout is evaluated using basis-alternating repetitive measurements and consistency-based acceptance of consecutive readouts.
- Readout procedure: The first readout assigns the memory state, and the result is accepted only when consecutive readouts show a consistent pattern.Two different initial memory-qubit states are compared with a Monte Carlo model incorporating electrical readout effects.
VII. TELEPORTATION RESULTS
The numerical data underlying Figures 4b and 4c are provided in Tables VI and VII, respectively.
- Data availability: Numerical values for Figures 4b and 4c are listed in Tables VI and VII, respectively.These tables provide the data corresponding to the two main-text panels.
VIII. DATA ACQUISITION AND EXPERIMENTAL RATES
The conditional teleportation dataset comprised 2,272 events across six cardinal input states, collected in 79 measurement blocks over 21 days.
- 2,272 events were measured for conditional teleportation across six cardinal input states.The counts were |+X⟩382, |−X⟩385, |+Y⟩385, |−Y⟩378, |+Z⟩375, and |−Z⟩367.
- 79 approximately one-hour data blocks were acquired over 21 days.
IX. MODEL OF THE TELEPORTED STATE
The teleported-state model incorporates imperfections in entanglement, memory preservation, state operations, readout, decoupling, and ionization, with parameters summarized in Tables VIII and IX.
- The model includes imperfect Bell states on both Alice–Bob and Bob–Charlie links.
- Memory errors include Bob’s dephasing during Bob–Charlie entanglement generation and depolarizing noise on Bob’s and Charlie’s memory qubits.The depolarizing noise is attributed to imperfect initialization and swap gates.
- Readout errors on Bob’s and Charlie’s communication and memory qubits can produce incorrect feed-forward operations after Bell-state measurements.
- The model also includes depolarizing noise on Alice during decoupling and Alice’s ionization probability.
- Tables VIII and IX summarize input parameters and the estimated effects of the different error sources.
X. EFFECT OF THE 3 KEY INNOVATIONS ON THE TELEPORTED STATE FIDELITY AND EXPERIMENTAL RATE
The paper evaluates the innovations by comparing estimated teleported-state fidelity and experimental rate against baseline parameters, while accounting for state-preparation imperfections.
- The innovation analysis estimates average state fidelity and experimental rate using baseline parameters from prior performance.The simulation uses a 1000-entanglement-attempt timeout for the Bob–Charlie link.
- A 1000-entanglement-attempt timeout is applied to the second link before the protocol aborts and restarts.
- Approximately 0.995 is the estimated state-preparation fidelity averaged over the six cardinal states.Preparation errors are estimated as pinit = 1.2 × 10^-3 and pMW = 8 × 10^-3.
XII. CALCULATION OF TELEPORTED STATE FIDELITY WITHOUT FEED-FORWARD OPERATION
The supplementary material documents the teleportation circuit, memory-qubit and entanglement-generation parameters, error models, and numerical data used to calculate teleported-state fidelity without feed-forward operations.
- Protocol circuit: The full gate circuit specifies the sequence of operations used by the teleportation protocol.
- Memory-qubit parameters: The memory-qubit table defines magnetic-field, nuclear-precession, hyperfine-interaction, and pulse-sequence parameters for each setup.
- Entanglement-generation errors: The error tables quantify double optical excitation and double |0⟩ occupancy as per-node entanglement-generation error probabilities.Extra-photon detection enables real-time rejection of false heralding events associated with both mechanisms.
- Numerical model: The numerical model includes imperfect link Bell states, memory dephasing and depolarization, readout errors, Alice’s decoupling noise, and ionization.
- Fidelity and rate data: The supplementary tables provide numerical values for the fidelity and rate data displayed in the main-text teleportation figures.