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Metropolitan-scale heralded entanglement of solid-state qubits

Arian J. Stolk, Kian L. van der Enden, Marie-Christine Slater, Ingmar te Raa-Derckx, Pieter Botma, Joris van Rantwijk, Benjamin Biemond, Ronald A. J. Hagen, Rodolf W. Herfst, Wouter D. Koek, Arjan J. H. Meskers, René Vollmer, Erwin J. van Zwet, Matthew Markham, Andrew M. Edmonds, Jan Fabian Geus, Florian Elsen, Bernd Jungbluth, Constantin Haefner, Christoph Tresp, Jürgen Stuhler, Stephan Ritter, Ronald Hanson

arXiv:2404.03723v1quant-ph

TL;DR

Long-range entanglement must be delivered live to nodes for further quantum-information use. The paper demonstrates fully heralded delivery over a deployed metropolitan link using real-time processing of heralding signals. The delivered states have fidelity 0.534(15), and the authors identify signal-to-noise ratio as a current fidelity limitation.

  • Problem

    Long-range entanglement must be delivered live to nodes for further quantum-information use, rather than merely identified in post-processing.

    Source: §III · p. 5

  • Method

    The deployed link uses full heralding and real-time processing of heralding signals to deliver entangled states to the nodes.

    Source: §III · pp. 5–6

  • Results

    The delivered entangled states have a fidelity of 0.534(15), establishing a metropolitan-scale demonstration with heralding signals processed in real time.

    Source: §III · p. 6

  • Takeaways & Limitations

    The architecture is directly applicable to other qubit platforms using photon interference and frequency conversion, and phase-locking remote signals may also be useful for ensemble-based quantum memories.

    Source: §IV · p. 7

    Signal-to-noise ratio currently limits the entangled-state fidelity, contributing about 30%.

    Source: §IV · p. 7

Abstract

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A key challenge towards future quantum internet technology is connecting quantum processors at metropolitan scale. Here, we report on heralded entanglement between two independently operated quantum network nodes separated by 10km. The two nodes hosting diamond spin qubits are linked with a midpoint station via 25km of deployed optical fiber. We minimize the effects of fiber photon loss by quantum frequency conversion of the qubit-native photons to the telecom L-band and by embedding the link in an extensible phase-stabilized architecture enabling the use of the loss-resilient single-photon entangling protocol. By capitalizing on the full heralding capabilities of the network link in combination with real-time feedback logic on the long-lived qubits, we demonstrate the delivery of a predefined entangled state on the nodes irrespective of the heralding detection pattern. Addressing key scaling challenges and being compatible with different qubit systems, our architecture establishes a generic platform for exploring metropolitan-scale quantum networks.

I. DEPLOYED QUANTUM NETWORK LINK ARCHITECTURE

The link combines telecom conversion, single-photon heralding, and active stabilization to connect independently operated diamond-spin nodes over deployed fiber. Feedback controls timing, phase, and polarization, including adjustments that tune the entangled-state phase.

I. DEPLOYED QUANTUM NETWORK LINK ARCHITECTURE

  • Each node's NV-center transition at 637 nm generates qubit-photon entanglement, while resonant laser light and microwave pulses initialize, read out, and control the qubit.A micro-controller and arbitrary waveform generator coordinate and shape the experiment's laser and microwave pulses.Source: §I · p. 2, Figure 2 · p. 3
  • Independent quantum frequency converters shift 637 nm photons to the telecom L-band at 1588 nm, reducing deployed-fiber loss and tuning the nodes to a common wavelength despite few-gigahertz emission offsets.The Delft NORA converter produces two orders of magnitude fewer background counts than the ppLN-based converter in The Hague.Source: §I · p. 2
  • The single-photon protocol interferes photons at the midpoint and heralds a Ψ± spin state upon single-photon detection; its entangling rate scales favorably with the square root of link transmission.The sign depends on the detector output arm, and the state phase depends on the optical phase difference of the arriving photons.Source: §I · p. 2
  • At a 100 kHz heartbeat, stabilization light is sent continuously except during the 2 µs interval for entangling photons, enabling near-continuous feedback during entanglement generation.Five phase-locking loops stabilize optical phase, with midpoint feedback bandwidth exceeding 200 kHz.Source: §I · pp. 2–3
  • Timing adjustments every ∼15 minutes keep offsets below 50 ps, limiting entangled-state infidelity from fiber-length drift to below 0.1%.The offsets are much smaller than the photon 1/e decay time of 12 ns.Source: §I · p. 3
  • Phase stabilization over 24 hours has a few-percent fidelity impact; polarization feedback keeps alignment within a few percent, with residual mismatch costing some rate.QFC-pump feedback updates at 500 Hz to accommodate observed frequency drifts above 50 MHz.Source: §I · p. 4

II. POST-SELECTED ENTANGLEMENT GENERATION OVER A DEPLOYED LINK.

The deployed link generates post-selected entanglement between remote solid-state qubits, with fidelity above the entanglement threshold and a rate that increases as the photon-acceptance window widens. Because detection is used in post-processing after qubit measurement, these states are not available for further use.

II. POST-SELECTED ENTANGLEMENT GENERATION OVER A DEPLOYED LINK.

  • Post-selection measures the qubits directly after spin-photon entanglement and uses midpoint photon detections in post-processing; the scenario is compatible with quantum key distribution but does not deliver reusable entangled states.Each node first passes a charge-resonance check, then stabilizes its local phase and attempts entanglement once per 10 µs heartbeat.Source: §II · p. 5
  • Correlations measured in different readout bases show the expected (anti-)correlations and agree with the detailed model, which has no free parameters.The two detectors herald Ψ+ or Ψ− states, giving opposite signs for the XX and YY correlations.Source: §II · p. 5
  • F(|Ψ±⟩) > 0.5, proving post-selected two-qubit entanglement over the deployed link.The fidelity is calculated from the ⟨ZZ⟩, ⟨XX⟩, and ⟨YY⟩ correlators; Fig. 3B shows the measurements.Source: §II · p. 5
  • The entangled-state fidelity decreases slowly as the photon-acceptance window widens, following the midpoint detection signal-to-noise ratio.A wider window accepts more photon detections and increases the success rate.Source: §II · p. 5
  • 0.48 Hz is the achieved entanglement generation rate for a 20 ns window, with success probability per attempt of 7.2 · 10−6.Source: §II · p. 5

III. FULLY HERALDED ENTANGLEMENT GENERATION OVER A DEPLOYED QUANTUM LINK

The nodes preserve their qubits while heralding information travels from the midpoint, then use real-time feedback to deliver the same Bell state for either detector outcome. The experiment demonstrates fully heralded metropolitan-scale entanglement, with delivery rate constrained by the communication delay.

III. FULLY HERALDED ENTANGLEMENT GENERATION OVER A DEPLOYED QUANTUM LINK

  • Echo refocusing preserves the qubits while heralding signals travel to the nodes, with the selected first echo revival marking entanglement delivery.The wait reduces coherence by 1.3% at Delft and 3.2% at The Hague.Source: §III · p. 5
  • Detector identity is processed in real time, enabling feed-forward to deliver the same Ψ− state for either heralding outcome.Nodes retry until successful heralding, then apply basis-selection gates and perform single-shot readout.Source: §III · p. 5, Figure 4 · p. 6
  • 0.534(15) fidelity was measured for entangled states delivered ready for further use after real-time processing of all heralding signals.The correlations show expected anti-correlated outcomes in all three bases; Fig. 4C shows both detector outcomes delivering the same Ψ− state.Source: §III · pp. 5–6, Figure 4 · p. 6
  • 0.022 s−1 (1.3 min−1) is the entanglement generation rate at the predefined 15 ns acceptance window.Communication delay makes each attempt approximately 20 times slower than in the post-selected case; the rate-fidelity trade-off is shown in Fig. 4D.Source: §III · p. 6, Figure 4 · p. 6

IV. CONCLUSION AND OUTLOOK

The work demonstrates heralded entanglement delivery between solid-state qubits at metropolitan scale and describes improvements that could raise fidelity and extend the network. The architecture is presented as applicable to other qubit platforms and potentially useful for ensemble-based memories.

IV. CONCLUSION AND OUTLOOK

  • The deployed link demonstrates heralded entanglement delivery between solid-state qubits at metropolitan scale.The authors state that the architecture and methods apply to other platforms using photon interference and frequency conversion.Source: §IV · p. 7
  • The current signal-to-noise ratio limits entangled-state fidelity, while proposed hardware and coherence improvements are projected to raise it above 90%.The authors also describe extending the architecture beyond two nodes, in combination with local memory qubits, to explore more advanced metropolitan-scale protocols.Source: §IV · p. 7

S1. EXPERIMENTAL SETUP

The experimental setup builds on previously described hardware and software, with a changed quantum device and laser at the Hague node to support phase stability between separated setups.

S1. EXPERIMENTAL SETUP

  • The experimental setups build on hardware described in Ref. and use software based on the Quantum Measurement Infrastructure.The framework is used to control laboratory equipment.Source: S1. EXPERIMENTAL SETUP · p. 11

A. Quantum Node

  • The Hague node received a newly fabricated diamond device and an upgraded 637 nm laser with optical feedback to reduce phase noise below 40 mrad integrated from 100 kHz to 100 MHz.The device substrate and parameters, including purity, crystal orientation, and carbon isotopes, match those previously reported.Source: A. Quantum Node · p. 11

B. Quantum Frequency Converters

The setup combines frequency conversion, node and midpoint phase control, and heralding feedback to support metropolitan-scale entanglement. Its stabilization scheme separates fast incoming-light control from slower relative-phase correction.

B. Quantum Frequency Converters

C. Phase stability on the nodes

  • A local interferometer locks the excitation-laser path to the node’s stabilization path, with integral frequency feedback limiting the free evolution time of local phase stability.The authors propose replacing the actuator with a linear phase shifter to improve local phase stability.Source: C. Phase stability on the nodes · p. 11

D. Midpoint

  • The midpoint redesign targets noise, crosstalk, detector background, and photon loss while supporting faster phase feedback.Changes include split reference-light paths, detector-shielding attenuators, polarization controllers, phase-control AOMs, and removal of a circulator; stabilization error signals share a balanced photodiode.Source: D. Midpoint · p. 12

E. Heralding

  • The midpoint FPGA accepts detections within a heartbeat-timed window and sends separate heralding and detector-identity pulses aligned to arrive at the nodes modulo the 10 µs heartbeat.The acceptance timing is derived from the centralized clock and heartbeat signal.Source: E. Heralding · p. 12

S2. PHASE STABILIZATION IN THE MIDPOINT

  • The stabilization scheme locks incoming light from each node to a common telecom reference and stabilizes relative phase through interference at the midpoint beam splitter.The relative phase is measured with the SNSPDs.Source: S2. PHASE STABILIZATION IN THE MIDPOINT · p. 12

A. Fast stabilization

  • Fast stabilization synchronizes each node’s incoming light to a reference with feedback bandwidth above 200 kHz, while slower QFC feedback compensates frequency drift.The QFC feedback operates at 500 Hz and accommodates frequency range greater than 1 GHz.Source: A. Fast stabilization · pp. 12–13

B. Global stabilization

  • Global stabilization uses interference of the nodes’ stabilization light at the central beam splitter to correct phase drift and set the relative phase.A detector-count difference produces a heterodyne beat that is compared with a reference to generate the feedback error signal.Source: B. Global stabilization · p. 13

C. Verifying phase stability

The link verifies phase stability through interference of the nodes’ excitation lasers at the midpoint. Its timing, polarization, and filter-stabilization procedures coordinate photon interference and detection across the deployed link.

C. Verifying phase stability

  • Interference of the nodes’ excitation lasers at the midpoint provides an error signal for verifying optical phase stabilization, with contrast evaluated after correcting for photon-flux imbalance.Changing the reference phase measures a full visibility fringe; a fuller technical analysis is deferred to a separate manuscript.Source: C. Verifying phase stability · p. 13

A. Pulses and timing at node

  • A shared midpoint clock aligns entanglement attempts, while heralded attempts place the interval before basis selection at a spin-coherence revival.The timing sequence otherwise contains the same pulses as an attempt without heralding.Source: A. Pulses and timing at node · p. 13

B. Pulses and timing at midpoint

  • The midpoint uses about 8 µs for phase, frequency, and filter stabilization, then opens the photon path to the detectors during the remaining ∼2 µs.During the photon window, the local reference light is off and the phase Track-and-Hold amplifier is set to hold.Source: B. Pulses and timing at midpoint · p. 13

C. Time-of-arrival alignment

  • Photon arrival-time alignment is needed for mode overlap at the midpoint; unequal fiber lengths require delayed starts and sub-heartbeat timing adjustments.Delft sends as soon as possible while The Hague holds its pulse-sequence start for three heartbeats; an AWG adjusts timing in the final ∼2 µs.Source: C. Time-of-arrival alignment · p. 14
  • A manual arrival-time calibration is followed by automatic AWG skew adjustments about every 15 minutes using the time-synchronization system’s change in fiber time of flight.The initial timing difference is measured at the midpoint timetagger and recorded as a calibration parameter.Source: C. Time-of-arrival alignment · p. 14

A. Polarization stabilization

  • An error signal based on polarization overlap with an in-fiber polarizer drives gradient-ascent feedback to stabilize the incoming light’s polarization.The loop uses a phase-gain detector to monitor beat amplitude and commands the electronic polarization compensator.Source: A. Polarization stabilization · p. 14

B. Ultra-narrow FBG stabilization

  • A heterodyne beat measurement stabilizes the ultra-narrow fiber Bragg gratings with only ≈10 fW of backward-traveling light.The method is more sensitive than a DC power measurement and reduces reflected optical power toward the SNSPDs.Source: B. Ultra-narrow FBG stabilization · p. 14

S5. DEPLOYED FIBER CHARACTERIZATION AND STABILITY

The deployed fiber link’s length and loss changed during network restructuring, and its losses exceeded ideal-fiber values. A modular system allowed propagation-delay realignment as conditions changed.

S5. DEPLOYED FIBER CHARACTERIZATION AND STABILITY

  • Deployed-fiber losses exceeded the ideal ≈0.2 dB km−1 at 1580 nm and varied across fiber sections; restructuring changed length by ±100 m and loss by ±1 dB over several weeks.Table S2 is identified as reporting parameters of the quantum link; its values are not included in the supplied passage.Source: S5. DEPLOYED FIBER CHARACTERIZATION… · p. 14, Table S2 · p. 15
  • The modular system allows photon arrival time at the midpoint to be realigned after fiber restructuring and daily expansion or contraction.Source: S5. DEPLOYED FIBER CHARACTERIZATION… · p. 14

A. Entanglement generation

Entanglement generation is interleaved with calibrations of signal-to-noise ratio, optical phase stability, and entangled-state phase. These measurements set and feed forward phase conditions for the generated state.

A. Entanglement generation

  • Three interleaved calibrations measure signal-to-noise ratio, optical phase stability, and entangled-state phase before correlators are measured for fidelity.The calibration sequence proceeds to fidelity measurements when its thresholds are passed.Source: A. Entanglement generation · p. 15
  • The signal-to-noise calibration measures single-photon signals from both nodes and background, including system losses.The sequence prepares the communication qubit in |0⟩ for signal measurement and uses a π-rotation to measure noise.Source: A. Entanglement generation · p. 15
  • Interfering a bright excitation-laser pulse measures the relative optical-phase fringe and residual phase noise; its setpoint can be chosen to optimize entangled-state fidelity.The reported setpoints include 0° and 180°.Source: A. Entanglement generation · p. 15
  • The entangled-state phase is measured from spin-spin correlations and fed forward to generate Ψ± = 1/√2 (|01⟩± |10⟩) during entanglement generation.This phase has an offset relative to the optical-phase setpoint.Source: A. Entanglement generation · p. 15

B. Experimental setup performance

The setup uses calibrations on daily and shorter timescales to maintain performance and detect drift. Measurements outside acceptance bounds or reduced CR-check passing rates trigger recalibration.

B. Experimental setup performance

  • Communication-qubit performance parameters, including laser power and the optical excitation π pulse, are recalibrated daily.Source: B. Experimental setup performance · p. 15
  • About every 20 minutes, shorter-timescale calibrations run, and measurements outside acceptance bounds restart the calibration sequence.Source: B. Experimental setup performance · p. 15
  • FID data taking stops when the CR-check passing rate falls below its SNR-sequence average, because the rate reflects underlying setup parameters that may have drifted.The calibration sequence then restarts from the SNR measurement.Source: B. Experimental setup performance · p. 16

S7. MODELING THE GENERATED ENTANGLED STATE

A Monte Carlo model estimates entangled-state outcomes from detection patterns while accounting for optical and experimental imperfections. The modeling also incorporates ionization as a third qubit level and explores simulated near-term link improvements.

S7. MODELING THE GENERATED ENTANGLED STATE

  • The Monte Carlo model in computes detection-pattern probabilities and corresponding spin states to estimate the average entangled-state density matrix, including optical and experimental imperfections.It considers events with at most two photons reaching the central detectors, photon loss and indistinguishability, wavepacket shape, phase and dephasing noise, and dark counts.Source: S7. MODELING THE GENERATED ENTANGLED… · p. 16
  • The fidelity model includes uncorrected ionization by treating an ionized node as a third level outside microwave control that reads as |1⟩, with probability p_ion.The model assumes a detected node photon rules out ionization at that node, while the other node may be ionized; noise-photon events allow either node to be ionized.Source: S7. MODELING THE GENERATED ENTANGLED… · p. 16
  • Near-term link performance is simulated with SnV centers, retaining collection efficiency while assuming 16 times higher coherent photon emission probability per optical excitation, improved QFCs, and improved phase stability.The simulations also describe future improvements including dynamical decoupling, reduced double excitation and ionization, and improved beamsplitter mode overlap.Source: S7. MODELING THE GENERATED ENTANGLED… · p. 16, Table S4 · p. 18
  • The error budget reports each infidelity contribution as if that error acted alone, while noise counts make the combined simulated infidelity differ from the sum of contributions.Table S3 covers post-selected and heralded states; photon-detection probability is given for α = 1.Source: Table S3 · p. 17
  • FPGA-processed photon detections inside the heartbeat-derived acceptance window trigger heralding signals to both nodes, while full-heralding measurements examine correction independent of detector outcome.The measurement also varies the photon acceptance-window length to compare fidelity and entanglement generation rate.Source: Figure S6 · p. 23, Figure S9 · p. 25
  • The experiment’s calibration cycle checks signal-to-noise, phase, and entangled-state phase parameters before fidelity measurements, with thresholds determining whether the sequence continues.Frequency, phase, polarization, and time-of-flight data are logged centrally; the phase-lock system uses feedback to stabilize the relative optical phase between nodes.Source: Figure S1 · p. 19, Figure S7 · p. 24, Figure S10 · p. 26
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