Demonstration of quantum network protocols over a 14-km urban fiber link

The study addresses the challenge of distributing high-fidelity quantum states across deployed urban fiber networks, which are subject to environmental perturbations (wind, rain, ice, thermal fluctuations) causing polarization mode dispersion, time-of-flight fluctuations, and polarization-dependent loss. The research question is whether polarization-encoded photonic qubits can be reliably transmitted over a 14.4 km urban fiber link with sufficient stability and fidelity to enable quantum networking protocols. The purpose is twofold: (1) to characterize the urban fiber as a quantum channel (loss, background light, polarization-dependent loss, polarization drift, time jitter, and phase stability), and (2) to demonstrate core quantum networking protocols—photon-photon entanglement distribution, ion-photon entanglement via heralded absorption, and ion-to-photon quantum state teleportation—using a trapped 40Ca+ memory, an SPDC entangled photon source, and polarization-preserving quantum frequency conversion to the telecom C-band. The importance lies in validating deployed urban fiber infrastructure for polarization-encoded quantum communication with active stabilization, paving the way for scalable metropolitan quantum networks.

The work builds on prior characterization of deployed quantum network testbeds (e.g., the Boston-area 50-km testbed) and field demonstrations of entanglement distribution and QKD over metropolitan fibers. It references methods and challenges related to polarization mode dispersion, polarization-dependent loss, and environmental effects in installed fibers. Compared to prior efforts, this study integrates a trapped-ion quantum memory with an SPDC source and telecom-band frequency conversion across a deployed urban link and implements active polarization stabilization tailored to polarization qubits.

- Fiber link and roles: Two dark fibers between Saarland University (UdS) and htw saar (Saarbrücken, Germany) are used: Link-Q (quantum) and Link-C (classical/control). The 14.4 km path includes underground segments, a 1278 m overhead segment, and multiple patch stations. - Loss characterization: Optical time-domain reflectometry (OTDR) at 1550 nm measured total loss of 10.4 dB (Link-Q) and 8.9 dB (Link-C), including several patches and a faulty splice at 6.6 km causing 4.1 dB (Link-Q) and 2.8 dB (Link-C) loss. Bare fiber attenuation: 0.19–0.23 dB/km. - Background light: Superconducting nanowire single-photon detectors (SNSPDs, >80% efficiency at 1550 nm) measured significant uncorrelated day/night fluctuations attributed to patch-station activity or neighboring fibers. A broadband-suppression filter (variable Bragg grating + Fabry–Pérot, 250 MHz passband) at htw reduced mean background to 19.7 s^-1 including dark counts. - Polarization-dependent loss (PDL): PDL of the looped link (UdS→htw→UdS) measured using two polarization scramblers (waveplates + piezo controller) to find L_tot and subtract detection PDL L_det. One-way PDL inferred as L = (L_tot - L_det)/2 assuming uniform contributions. Over ~6 days, L_rot = 0.39(7) dB (full loop including detection) and L_det = 0.23(2) dB, yielding one-way fiber PDL L = 0.08(9) dB. From this PDL a lower bound on process fidelity F_p ≥ 0.991 was estimated. - Quantum channel modeling and polarization drift: The single-qubit channel is described by a time-dependent rotation M(t) (offset γ ≈ 0 due to negligible depolarization), with process fidelity F_p(t) = (1 + tr(M(t)))/4. Alternating reference lasers prepared in H and D polarization are injected to reconstruct M via measured Stokes vectors and Eq. for tr(M). A 7-day drift measurement showed stronger daytime fluctuations; quantiles of F_p(τ) vs time separation τ determine how long free drift can be tolerated before re-stabilization. - Temporal spread and path-length stability: • Coincidence wave-packet method: Using the same SPDC source as in protocols, compare arrival-time correlations with both photons local vs one photon converted to 1550 nm and sent over Link-Q to htw (with return time-stamping over Link-C). Fiber-induced jitter bounded < 600 ps over 80 s integration. • Interferometric method (Menlo Systems): A 1500 nm laser sent over Link-C, frequency-shifted by an AOM and retroreflected; beat note at UdS analyzed with a frequency counter (10 ms gate). Doppler-induced frequency shifts mapped to time delay ΔT, tracked over 12 days. Measured drift correlates with expected values from SMF-28 temperature sensitivity (37.4 ps km^-1 K^-1) and ambient temperature data; enables future active stabilization of optical path length. - Experimental setups: • Polarization detection at htw: 250 MHz bandpass filter (BPF), motorized quarter-/half-waveplates, Wollaston prism, two SNSPDs. Detector outputs are converted to optical pulses, sent via Link-C using CWDM, reconverted and time-tagged at UdS. • Polarization stabilization: Sender injects two reference beams (H and D) via MEMS switching and fiber splitters into Link-Q. Receiver uses a piezo polarization controller and MEMS switching to alternate between a polarimeter (for stabilization) and the detection setup (for communication). A gradient-descent feedback algorithm adjusts four piezo voltages to minimize deviation from target Stokes vectors. One full correction run: ~1.1(5) s, eight feedback iterations (~90 ms each). Stabilization runs interleaved with measurements. • SPDC source and QFC: Type-II cavity-enhanced SPDC produces entangled photons with state |Ψ⟩ = |H⟩_A|V⟩_B − e^{-iφ}|V⟩_A|H⟩_B. Arm A photon: 854 nm, resonant with 40Ca+ D5/2–P3/2, 12.29 MHz bandwidth. Arm B photon detuned by 480 MHz and converted to 1550 nm via polarization-preserving difference-frequency generation in a Sagnac-configured PPLN waveguide. Narrowband filtering (250 MHz) reduces conversion noise to 24 s^-1; external device efficiency 57.2% including filters. For experiments φ = 0° to prepare |Ψ+⟩. • Ion trap (UdS): Linear Paul trap with a single 40Ca+ ion (NA 0.4 objectives) for 854 nm absorption and 393 nm detection. Laser/RF pulses provide state preparation, spin-echo, and projective readout. Photodetectors time-tagged. • Basis calibration: Automated periodic calibration (every 30 min for 90 m fibers UdS→QFC and every 2 h for 854 nm path A) using single-photon states (H and converted to R) to correct slow drifts in unstabilized fiber segments. - Protocol implementations: • Photon-photon entanglement distribution: Continuous SPDC; arm A analyzed locally, arm B converted and sent over Link-Q to htw; two-qubit state tomography (16 settings). Stabilization threshold F_p,th = 99%; basis recalibration as above. • Ion–photon entanglement: Heralded, state-preserving absorption of the 854 nm photon by the ion maps photonic qubit (arm A) to the ion’s Zeeman qubit; partner photon (arm B) converted and sent to htw. Ion exposure window 400 μs with spin-echo. • Teleportation: Prepare an arbitrary ion memory qubit; perform a Bell-state measurement via heralded absorption and projective measurements; teleport the memory state onto the remote 1550 nm photon at htw. Quantum process tomography conditioned on two BSM outcomes to determine required Pauli corrections.

- Loss and noise: • Total attenuation: 10.4 dB (Link-Q), 8.9 dB (Link-C); faulty splice at 6.6 km adds 4.1 dB (Link-Q) and 2.8 dB (Link-C). Bare fiber attenuation 0.19–0.23 dB/km. • Background after 250 MHz filter: 19.7 s^-1 (incl. dark counts). - Polarization characteristics: • One-way PDL L = 0.08(9) dB; implies process fidelity F_p ≥ 0.991 from PDL bounds; PDL time trace indicates minimum process fidelity remains well above 98% except for occasional spikes. • Polarization drift: Daytime fluctuations stronger than nighttime. After stabilization to F_p,th = 99%, with 90% certainty F_p > 98% for up to 176 s (full link plus stabilization components). Free drift characterization guides re-stabilization scheduling. - Temporal stability: • Fiber-induced arrival-time jitter < 600 ps (80 s integration) compared to local measurement. • 12-day interferometric path-length monitoring shows ΔT drifts matching predictions from SMF-28 thermal sensitivity and ambient temperature, dominated by the 2 × 1278 m overhead segment. - Stabilization performance: • One full polarization correction run: 1.1(5) s with 8 feedback iterations; typical recovery from arbitrary rotation to F_p,th = 99% in t ≈ 6.4(1.7) s; from F_p ≈ 96% in t ≈ 3.3(0.6) s. Duty cycle example: 100 s transmission / 1.1 s stabilization ≈ 91. - Entangled-pair source and link transmission: • With pump power 15 mW: detected 854 nm–854 nm local coincidence rate 3352.0 s^-1; 854 nm (UdS) – 1550 nm over link (htw) 144.4 s^-1; background 2.32 s^-1 (local) and 0.12 s^-1 (remote). Effective coincidence reduction 13.66 dB. Component losses to htw sum to 22.73 dB (including: QFC+lab transmission 6.78 dB; Link-Q 10.4 dB; stabilization sender 0.46 dB; receiver 1.3 dB; filtering+projection 0.65 dB; detector 0.97 dB; residual 2.17 dB due to connections/misalignment). - Photon–photon entanglement over the link: • Two-qubit tomography shows background-corrected Bell-state fidelities F > 98% for wait times up to 60 s between stabilization runs; slow decrease beyond 60 s attributable to fiber-induced drifts. Minor reduction vs laboratory benchmarks attributed mostly to PDL. - Ion–photon entanglement over the link: • Tomography (ion Zeeman basis |S1/2, m=±⟩; photon |R/L⟩): fidelity to |φ⟩_(ph,at) = (|−⟩|R⟩ − |+⟩|L⟩)/√2 is 79(2)% raw, 83(2)% background-corrected; state purity 71(3)% raw, 79(4)% corrected. Reduced vs direct ion–photon entanglement benchmarks due to added system complexity, longer integration and stability demands, and exposure/decoherence trade-offs. - Ion-to-photon teleportation over the link: • Process tomography conditioned on two BSM outcomes shows required corrections: identity (|−⟩) and σ_z (|+⟩). Process fidelities: 78(6)% and 86(5)% raw; 80(6)% and 87(5)% background-corrected. - Reach estimation with optimized fiber: With 0.2 dB/km attenuation and similar system losses, ≈52 km at current coincidence rates; ≈150 km until coincidences reach background level.

The characterization confirms that a heterogeneous urban dark-fiber link (including overhead spans and multiple patches) can serve as a stable polarization qubit channel. Low polarization-dependent loss and bounded time jitter enable high process fidelity operation without continuous control for tens to hundreds of seconds. Active polarization stabilization, running in an interleaved mode with a short correction time, maintains high-fidelity transmission with a practical duty cycle. Applying this channel to quantum networking primitives, the work shows: (i) high-fidelity photon–photon entanglement distribution to a remote node, (ii) distant ion–photon entanglement via heralded, state-preserving absorption, and (iii) ion-to-telecom-photon quantum state teleportation with process fidelities consistent with laboratory-level benchmarks once background is accounted for. The results demonstrate that integrating a trapped-ion memory, narrowband SPDC source, and polarization-preserving QFC with deployed fibers preserves essential quantum figures of merit, validating the approach for metropolitan quantum networks. Remaining drifts (polarization and phase) and sporadic PDL spikes point to environmental influences (especially on overhead sections), motivating adaptive scheduling of stabilization and potential future phase stabilization—particularly relevant for interference-based protocols. The demonstrated performance suggests feasibility for near-term implementations of QKD, remote memory entanglement, and repeater building blocks over urban fiber.

This work demonstrates that a 14.4 km deployed urban fiber link, equipped with active polarization stabilization, supports polarization-encoded quantum networking protocols. The link was thoroughly characterized (loss, background, PDL, polarization drift, timing stability), and practical stabilization achieved a high duty cycle while keeping process fidelity near 99% over typical operation windows. Using a cavity-enhanced SPDC source, a trapped 40Ca+ ion memory, and polarization-preserving telecom-band frequency conversion, the team realized: high-fidelity entanglement distribution over the link, distant ion–photon entanglement via heralded absorption, and ion-to-photon quantum teleportation with process fidelities up to ~87% (background-corrected). These proof-of-concept demonstrations indicate that deployed metropolitan fibers can support advanced quantum protocols with matter–light interfaces. Future directions include investigating and mitigating time-dependent PDL and phase fluctuations, implementing active phase stabilization for interference-based protocols, extending distances with optimized links, integrating feed-forward for real-time teleportation corrections, and pursuing QKD and remote memory entanglement toward quantum repeater architectures.

- Incomplete control of environmental perturbations on deployed fibers (especially overhead segments) leads to time-varying polarization rotations, occasional PDL spikes, and phase fluctuations, necessitating periodic stabilization and limiting free-drift intervals. - Background light coupled from neighboring fibers and infrastructure causes fluctuating counts; although filtered, it imposes constraints on achievable SNR and integration times. - Unstabilized internal fiber segments (e.g., between SPDC and QFC, local 854 nm paths) exhibit slow drifts that require periodic calibration and can contribute to phase drift of the entangled state. - Aggregated system complexity (SPDC + QFC + ion trap + deployed link) increases integration times and stability requirements, reducing ion–photon entanglement fidelity relative to direct laboratory benchmarks; exposure-time trade-offs are needed to balance success probability against ion decoherence. - The link used includes a faulty splice contributing substantial excess loss; while representative of real-world conditions, it limits current rates and distances; results are projected to improve with optimized infrastructure. - No active phase stabilization was implemented; for interference-based protocols, phase noise in the link could limit fidelity unless mitigated.