Structured leakage in OAM-encoded qubits revealed by distributed quantum feature extraction

AI summary

Overview

Research area: High-dimensional quantum communication and quantum channel characterization, specifically orbital angular momentum (OAM) encoding of photonic qubits propagating through atmospheric turbulence, combined with a quantum machine-learning (quantum convolutional) feature-extraction pipeline.

Technical level: Advanced. The paper assumes familiarity with Kraus/operator-sum channel representations, Laguerre–Gaussian mode bases, Kolmogorov turbulence phase screens, the angular-spectrum propagation method, and variational quantum circuit construction (PennyLane's RandomLayer).

One-sentence scope: The paper builds a logical-qubit model of OAM propagation through simulated and experimentally emulated turbulence, shows that degradation appears as structured leakage out of the encoded OAM subspace, and uses a distributed quantum convolutional circuit to extract turbulence-robust features from the resulting intensity patterns.

What This Paper Is About

OAM modes offer a very large Hilbert space for encoding quantum information in free space, but atmospheric turbulence mixes modes, introduces crosstalk, and reduces fidelity in ways that are usually summarized only by a single degradation number (fidelity, crosstalk, or error rate). The authors ask a deeper question: how does a turbulent channel redistribute OAM-encoded information, and does the redistribution leave a structured, detectable signature beyond the intended logical subspace? To answer this, they treat OAM modes as logical qubits evolving through noisy quantum channels, quantify the resulting "leakage," and then test whether a distributed quantum feature-extraction circuit can recover physically meaningful patterns from turbulence-degraded intensity images, both in simulation and in two optical experiments.

Key Contributions

1. A logical-qubit channel framework for OAM propagation. OAM modes with radial index p = 0 and azimuthal index ℓ are mapped onto logical qubit states, and turbulence is recast as an effective channel derived from the turbulence-induced scattering matrix, allowing direct comparison with standard quantum noise models (bit-flip, phase-flip, depolarizing, amplitude damping).

2. Identification and quantification of structured leakage. The authors define leakage as probability amplitude redistributed beyond the encoded OAM subspace and show it is not random: it depends systematically on turbulence strength (approximately linearly, after polynomial fitting) and on OAM order, using 100 turbulence realizations and a larger 10,000-realization study in Appendix B.

3. A distributed quantum feature-extraction pipeline. High-dimensional OAM intensity patterns are split into smaller patches and encoded into separate small quantum subsystems, reducing quantum resource requirements and mitigating encoding noise, then processed by a quantum convolutional operation (QConv) built from PennyLane's 9-wire RandomLayer as a quantum analogue of a 3×3 kernel.

4. Dual validation across discrete and continuous regimes. The leakage and distortion picture is confirmed both for reconstructed single-photon OAM qubits (SPDC bi-photon source) and for coherent continuous-wave beams (785 nm CW laser), with turbulence emulated by Kolmogorov phase screens on spatial light modulators in both cases.

Main Findings

• Scattering matrices spread off the anti-diagonal. At near-turbulence-free propagation (SR = 0.99) the scattering matrix is dominated by anti-diagonal components, meaning the field stays in its original OAM basis; as turbulence strengthens toward SR = 0.01, amplitudes populate neighboring modes and leakage emerges.

• Leakage grows with turbulence and with OAM order. Across 100 realizations spanning SR = 0.01 to 0.99, leakage follows an approximately linear trend with turbulence strength after polynomial fitting, and increases systematically with OAM order, so higher-order OAM states are more susceptible to degradation.

• A 10,000-realization check confirms the trend. Because the turbulence phase screen operator is stochastic, the authors repeat the analysis at much larger scale (Appendix B) and report persistent leakage trends with clearly distinguishable leakage regions for different OAM orders.

• Turbulence channels behave unlike CPTP channels. Conventional completely positive trace-preserving channels mainly rotate the reconstructed intensity pattern with limited deformation of the lobe structure, whereas turbulence-derived channels produce both rotation and substantial deformation, consistent with leakage out of the logical subspace.

• Turbulence resembles a mix of amplitude damping and depolarizing. The turbulence channel's fidelity and SSIM trends track the depolarizing channel closely, with minor differences at P_noise = 0.1, 0.2 and 0.5 in the fidelity plot and P_noise = 0.4 in the SSIM plot, and it also shows amplitude-damping-like behavior: slight rotation with destruction and partial reconstruction of superposition. Amplitude damping is found to be more noise-resilient than depolarizing.

• Order dependence differs between channel types. With 1 − P_noise fixed at 0.5, conventional channels degrade consistently as OAM order increases, while the turbulence channel shows an unstable increase at ℓ = ±2 and ±5.

• Simulated fidelity and SSIM stay high overall. In the discrete OAM-qubit simulation across ℓ = ±1 to ±6 at p = 0, overall trends sit above 0.6 (fidelity) and 0.7 (SSIM); order-dependent differences are distinct at lower SR (0.1 to 0.6) and minor at higher SR (0.7 to 1.0). Errors shrink as SR increases.

• Single-photon experiment agrees with simulation. Using an 810 nm SPDC source with turbulence on SLM2 and an ORCA-Quest qCMOS camera, measured feature maps show modest rotation with dominant turbulence-induced distortion; SSIM and fidelity remain in the range above 0.6 and 0.8 respectively, consistent with the turbulence-channel simulation. A reduced encoding dynamic range of L_data = 5 was used because of low photon flux and background noise near SR = 0.5.

• Continuous-wave experiment agrees too. With a 785 nm CW laser (SLM1 Santec SLM-200 for LG petal-beam generation, SLM2 for turbulence, Thorlabs CS2100M CCD for detection) and initial state |φ⟩ = (1/√2)(|0⟩ + i|1⟩), trends start from 0.4 in fidelity and 0.5 in SSIM; error ranges shrink mainly at SR = 0.8 and 0.9, and SSIM error is nearly unchanged with SR.

• Feature-space signatures survive degradation. Extracted feature maps retain contour information even when the raw intensity pattern is heavily distorted, supporting the claim that structured leakage leaves accessible signatures beyond the logical subspace.

Methodology in Plain English

The authors treat each pair of opposite OAM modes (for example ±ℓ) as the two states of a single qubit. They then simulate how a beam carrying such a state is distorted by atmospheric turbulence and read out what happens to the qubit.

Simulation side. They propagate a Gaussian beam on a 256 × 256 grid with 4 × 10⁻³ m sample length, waist 0.5 × 10⁻³ m, wavelength 785 nm, over 0.1 m using 5 turbulence phase screens, with ℓ_max = 12 and turbulence strengths from r₀ = 4.071 × 10⁻⁴ m to 1.608 × 10⁻² m (SR = 0.01 to 0.99). Propagation uses the angular-spectrum method with a Fresnel transfer function; turbulence is generated from a Kolmogorov phase power spectral density. The distorted field is projected onto Laguerre–Gaussian modes to build a scattering matrix. Two things are then extracted from that matrix: reconstructed OAM-qubit intensity patterns (treating matrix columns like mode-sorter outputs) and effective single-qubit operators built from four mode pairs ±ℓ, which act as the turbulence channel. Conventional noise channels are added for comparison using standard Kraus operators.

Experimental side. Kolmogorov phase screens are written onto spatial light modulators to create controlled, repeatable turbulence. One setup uses a 785 nm continuous-wave laser for the classical, continuous-space case; the other uses an 810 nm spontaneous parametric down-conversion bi-photon source for the single-photon, discrete-qubit case.

Feature extraction. Rather than encoding a full-resolution image into one large quantum state, each intensity image is cut into patches and encoded into small separate quantum circuits. Rotation-Y gates with dynamic range L_data = 8 (matching unsigned 8-bit images) encode pixel intensities, and a 9-wire RandomLayer circuit with seed 42 and nine parameters performs the convolutional step. Expectation values in the Z basis are measured to build feature maps, which are compared to ideal references using fidelity, the structural similarity index measure (SSIM), and the Strehl ratio as the optical measure of turbulence severity. Standard deviations are computed over the random turbulence matrices and over nine copies of the output features.

Why This Matters

The work reframes turbulence-induced OAM degradation from "noise that destroys signal" to "information that is redistributed in a structured, characterizable way." That shift gives experimentalists a quantitative channel-level diagnostic (leakage) rather than only an end-to-end fidelity number, and it links optical propagation physics to the language of open quantum systems, where comparison with standard noise channels becomes possible. It also shows that a quantum-native feature extractor can operate on data from real deployed hardware and still find usable structure.

Real-world applications:

• Free-space and satellite quantum key distribution: characterizing how much key material survives atmospheric links at a given turbulence level and OAM order.
• OAM-multiplexed optical communication: predicting which mode orders degrade first and should be avoided or adaptively reallocated in turbulent links.
• Adaptive optics and link budgeting: using leakage as a fast, physics-informed proxy for channel quality in optical ground stations.
• Quantum networking and entanglement distribution: understanding how turbulence reshapes entangled OAM states before they reach a repeater or memory node.

Industry relevance: relevant to satellite-to-ground quantum communication programs, free-space optical communications vendors, photonic quantum hardware groups building SLM- and OAM-based systems, and quantum software stacks (the pipeline is implemented with PennyLane and NumPy, so it sits inside existing variational-circuit tooling). The paper explicitly frames its goal as accessibility of signatures within quantum representations rather than classical computational advantage, which matters for groups deciding whether a quantum processor adds value to an optical channel-characterization workflow.

Future Directions

• Scaling to larger and more realistic settings. The discussion explicitly calls for extending the concepts to "larger, higher-dimensional, and more realistic scenarios" for robust characterization, information processing, and control of open quantum systems. The present study uses ℓ from ±1 to ±6 and a truncated 12-mode basis.
• Beyond the truncated logical subspace. The turbulence channel appears effectively non-trace-preserving within the truncated OAM basis, so a proper treatment of the full, unbounded OAM space and of the environment interaction (the authors defer the theoretical turbulence-channel construction to Section 4.9) remains open.
• A firmer link between optical and quantum noise parameters. The authors state that conventional noise parameters are not directly equivalent to the Strehl ratio, which makes distortion scales hard to compare across channel models; establishing that mapping is a natural next step.
• Hardware and encoding refinements. Experimental limitations (low photon flux, background noise, reduced dynamic range of 5 versus 8) and the untested effect of the radial index p (only p = 0 and p = 1 appear) point toward improved encoding strategies and multi-degree-of-freedom tests. Note that Appendices A through D, which contain the encoding framework, the 10,000-realization study, circuit initialization analysis, and fixed-phase-screen checks, are referenced but not included in the provided text.

Target Audience

Researchers and graduate students in quantum communication, free-space optical links, and structured light, especially those working on OAM-encoded quantum states, atmospheric channel modeling, or quantum machine learning applied to real optical data. It is also useful for experimentalists who emulate turbulence with spatial light modulators and want a channel-level diagnostic beyond fidelity, and for quantum-software practitioners interested in a distributed encoding scheme that keeps circuit width small when handling high-dimensional image data. Readers without a background in quantum channels or Fourier optics will find the methods section demanding.

Authors’ abstract

Orbital angular momentum (OAM) modes have emerged as an important platform for high-dimensional quantum communication but remain vulnerable to environmental noise and channel imperfections. Here we introduce a logical-qubit representation of OAM propagation in which modes evolve as qubits through noisy quantum channels. In this representation, turbulence manifests as leakage from the logical OAM subspace into turbulence-induced leakage components, providing a unified description of degradation in both single-photon and coherent-beam regimes. We show that turbulence-induced leakage exhibits systematic dependence on turbulence strength and OAM order, revealing structured signatures of information redistribution beyond the logical subspace. Leveraging this insight, we develop a distributed quantum feature-extraction scheme that encodes high-dimensional OAM states into quantum representations and employs quantum convolutional operations to extract turbulence-robust features. Simulations and experimental measurements demonstrate robust extraction of these features across a broad range of turbulence strengths, OAM orders, and propagation conditions. Our results establish a direct link between OAM-channel dynamics, structured leakage, and quantum learning, providing a physics-informed framework for characterizing turbulence-degraded high-dimensional optical states and extracting robust signatures of turbulence-induced information redistribution.