Quantum Parametric Mode Sorting LIDAR

• QPMS LIDAR is a lidar architecture that uses nonlinear, mode-selective optical processing to project optical returns onto engineered orthogonal modes.
• It leverages techniques like sum-frequency generation and quantum pulse gating to achieve high selectivity and in-band noise rejection across temporal and spatial bases.
• QPMS LIDAR offers promising applications in cloud calibration and photon-efficient target detection while facing challenges in scalability, synchronization, and environmental robustness.

Quantum Parametric Mode Sorting (QPMS) LIDAR denotes a class of lidar architectures in which optical returns are analyzed in a mode basis—temporal, spectral, spatial, or joint spatiotemporal—by using mode-selective processing before photodetection. In the literature considered here, the most explicit use of the term appears in a cloud-lidar calibration proposal based on sum-frequency generation (SFG) in a $\chi^{(2)}$ waveguide (Murchie et al., 22 Sep 2025). Closely related work establishes the underlying receiver primitives: programmable spatiotemporal parametric mode sorting by mode-selective quantum frequency up-conversion (Garikapati et al., 2022), multi-output time-frequency mode sorting with a quantum pulse gate (Serino et al., 2024), and high-selectivity temporal-mode interferometry based on cascaded quantum frequency conversion (Reddy et al., 2014). Taken together, these studies define QPMS LIDAR as a mode-aware sensing framework in which the receiver is designed not merely to filter in time or wavelength, but to project onto engineered orthogonal or hypothesis-specific optical modes.

1. Conceptual scope and distinguishing features

QPMS LIDAR is defined by the use of mode-selective optical processing rather than ordinary time gating or spectral filtering. The clearest statement of this distinction appears in the cloud-calibration proposal, which argues that the nonlinear conversion stage is selective to a particular temporal or spectral mode of the input signal and therefore provides “in-band noise-rejection beyond what linear noise filtering can provide” (Murchie et al., 22 Sep 2025). The same basic principle is expressed in the multi-output quantum pulse gate: the device is not simply a frequency demultiplexer, but a programmable projector onto selected time-frequency modes, with successful projections routed into distinct output-frequency channels (Serino et al., 2024).

In this literature, “mode sorting” does not denote a single measurement architecture. Some devices are fundamentally unitary sorters that map basis states to output ports, such as the fractional-Fourier-transform radial-mode sorter for Laguerre–Gaussian modes (Zhou et al., 2017). Others are better described as programmable nonlinear measurements. The multi-output quantum pulse gate is explicit on this point: in the ideal regime each channel is a projector $\pi^\gamma=\ket{\gamma}\bra{\gamma}$, but with non-unity conversion efficiency the device is described by a POVM with an additional inconclusive outcome (Serino et al., 2024). The spatiotemporal QPMS demonstration is similarly a matched nonlinear projection implemented by SFG and followed by single-photon detection, rather than a lossless universal unitary over all incident energy (Garikapati et al., 2022).

A practical consequence is that QPMS LIDAR is best understood as a receiver architecture for hypothesis-aligned mode discrimination. In some regimes it functions as a modal demultiplexer; in others it functions as a selective nonlinear gate that accepts one mode and rejects the rest. This distinction is central to how the approach is evaluated in ranging, imaging, and cloud-calibration settings.

2. Modal bases, orthogonality, and measurement structure

The modal language used in QPMS work is broader than simple time bins or wavelength bins. The time-frequency literature defines temporal modes as “field-orthogonal wave-packet modes” and emphasizes that frequency bins, time bins, and pulse modes are all realizations of this same object (Serino et al., 2024). In the same paper, Hermite–Gauss pulse modes are treated as orthogonal even though their intensity profiles overlap in both time and frequency, because orthogonality is carried by the full complex field.

The spatial literature makes the corresponding point for transverse structure. The Laguerre–Gaussian basis requires both azimuthal index $\ell$ and radial index $p$, and a full transverse characterization therefore requires access to both (Zhou et al., 2017). The radial sorter based on the fractional Fourier transform exploits the eigenvalue relation

$$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$

so that the mode-dependent phase can be converted into port-dependent interference (Zhou et al., 2017). This is the spatial analogue of the temporal-mode logic used in nonlinear frequency-conversion devices.

The measurement-theoretic structure of QPMS receivers is correspondingly diverse. For orthogonal mode sets, a sorter can realize parallel projective measurement by routing each mode to a distinct output. For non-orthogonal state sets, generalized measurements become necessary. A multi-plane-light-converter implementation of unambiguous state discrimination shows how a single passive optical network can perform a unitary in an enlarged Hilbert space and then spatially separate the conclusive outcomes and the inconclusive outcome (Goel et al., 2022). In the symmetric case treated there, the optimal unambiguous-discrimination success probability is

$\eta = 1-F,$

where $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$ is the common pairwise fidelity (Goel et al., 2022). This is directly relevant whenever a lidar receiver must discriminate overlapping return hypotheses.

Mode sorting is also tied to quantum-limited estimation. In incoherent imaging of a one-dimensional line object, pre-detection Hermite–Gaussian mode sorting achieves the quantum Fisher information for object-length estimation under a Gaussian point-spread function, whereas direct image-plane detection loses Fisher information per photon in the sub-Rayleigh regime (Dutton et al., 2018). A plausible implication is that QPMS LIDAR inherits not only a mode-demultiplexing role but also a quantum-measurement role: the receiver basis can determine whether available information is preserved or discarded.

3. Parametric mode-sorting mechanisms

The foundational nonlinear mechanism in QPMS is mode-selective quantum frequency conversion. In temporal-mode interferometry, two cascaded quantum frequency-conversion stages are arranged so that the target temporal mode experiences two approximately 50% conversions and therefore interferes like a Mach–Zehnder interferometer in frequency space (Reddy et al., 2014). The combined converted kernel is

$$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$

which makes explicit that one path corresponds to “stay in $s$, then convert,” while the other corresponds to “convert, then stay in $r$” (Reddy et al., 2014). This architecture raises temporal-mode selectivity from the single-stage limits of about $\pi^\gamma=\ket{\gamma}\bra{\gamma}$0 for three-wave mixing and about $\pi^\gamma=\ket{\gamma}\bra{\gamma}$1 for four-wave mixing to reported selectivities $\pi^\gamma=\ket{\gamma}\bra{\gamma}$2 for TWM-TMI and $\pi^\gamma=\ket{\gamma}\bra{\gamma}$3 for FWM-TMI in the cited configurations (Reddy et al., 2014).

The multi-output quantum pulse gate generalizes this logic to programmable time-frequency projections. Its frequency-domain transfer function is

$\pi^\gamma=\ket{\gamma}\bra{\gamma}$4

where $\pi^\gamma=\ket{\gamma}\bra{\gamma}$5 is the shaped pump function and $\pi^\gamma=\ket{\gamma}\bra{\gamma}$6 is the engineered phase-matching function (Serino et al., 2024). Multi-output operation is achieved by using a super-poled lithium-niobate waveguide with several phase-matching peaks, so that different programmed pump regions implement different projectors in parallel. In $\pi^\gamma=\ket{\gamma}\bra{\gamma}$7 and $\pi^\gamma=\ket{\gamma}\bra{\gamma}$8, detector tomography yielded average measurement fidelities up to $\pi^\gamma=\ket{\gamma}\bra{\gamma}$9 and $\ell$0, respectively, with single-photon-level input $\ell$1pulse (Serino et al., 2024).

The explicit spatiotemporal QPMS demonstration extends parametric sorting into a composite Hilbert space. The signal mode is written as

$\ell$2

with Laguerre–Gaussian spatial modes and Hermite–Gaussian temporal modes as the chosen basis (Garikapati et al., 2022). Selectivity is quantified by

$\ell$3

where $\ell$4 is the number of sum-frequency photons in the desired mode and $\ell$5 denotes the counts in all other considered modes (Garikapati et al., 2022). The reported discussion-level summary gives selectivities of $\ell$6 to $\ell$7 dB among two overlapping spatial modes and $\ell$8 to $\ell$9 dB among two overlapping temporal modes, with improvement up to $p$0 dB under temporal pump optimization (Garikapati et al., 2022). The paper further states that only optimizing the pump temporal profile can achieve more than $p$1 dB extinction for mutually unbiased-basis sets of spatiotemporal modes (Garikapati et al., 2022).

Two recurrent engineering principles appear across these nonlinear sorters. First, mode selectivity improves when the device operates near a favorable group-velocity regime: temporal-mode interferometry emphasizes group-velocity matching and controlled walkoff (Reddy et al., 2014), while the spatiotemporal QPMS device operates in the single side-band velocity-mismatch regime and benefits when the pump pulse is shorter than the pump–sum-frequency walkoff (Garikapati et al., 2022). Second, output filtering matters. The spatiotemporal QPMS paper reports improved performance by coupling the upconverted light into a single-mode fiber and by operating at the edge of phase matching (Garikapati et al., 2022), while the multi-output quantum pulse gate attributes much of its practical crosstalk to output spectrograph resolution rather than to the intrinsic phase-matching bandwidth (Serino et al., 2024).

4. Spatial subsystems and companion sorters in full QPMS receivers

Although QPMS is defined by nonlinear mode-selective conversion in many discussions, a full lidar receiver often requires additional linear spatial-mode subsystems. The radial Laguerre–Gaussian sorter based on the fractional Fourier transform fills a specific gap: efficient discrimination of the radial index $p$2 without sequential lossy projective filtering (Zhou et al., 2017). Its reported laboratory implementation sorted up to three separate radial modes in the restricted space $p$3, with measured total crosstalk $p$4 and an explicit caveat that “a priori knowledge about the input state is necessary for an appropriate sorting” (Zhou et al., 2017). The paper also stresses that the FRFT phase depends on both $p$5 and $p$6, so a pure radial sorter requires fixed $p$7, knowledge of $p$8, or an additional cancellation method such as a Dove prism (Zhou et al., 2017).

For arbitrary spatial bases, a graded-index multimode-fiber sorter offers a calibration-based alternative. Its programming rule is

$p$9

with $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$0 the measured transmission matrix, $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$1 the chosen input-mode basis, and $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$2 the target mapping matrix (Defienne et al., 2020). Experimentally, it sorted up to $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$3 modes of the Fourier basis and Laguerre–Gaussian-like phase basis, with average sorting ability $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$4 for a two-mode Fourier sorter but substantial degradation at larger dimension; for Fourier modes the reported values were $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$5 at $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$6, $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$7 at $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$8, and $$\mathcal{F}^{a}\!\left[\mathrm{LG}_{p\ell}(r_0,\theta_0)\right] = \exp\!\left[-i(2p+|\ell|)a\right] \mathrm{LG}_{p\ell}(r,\theta),$$9 at $\eta = 1-F,$0 (Defienne et al., 2020). The observed $\eta = 1-F,$1 degradation is a direct warning for high-dimensional receiver design.

Single-plane and diffractive-neural sorters show a different tradeoff. A single-plane analytic spatial sorter can separate Hermite–Gaussian, Laguerre–Gaussian, Bessel–Gaussian, and OAM families with average measured sorting efficiency $\eta = 1-F,$2 and average cross-talk $\eta = 1-F,$3 for tested four-mode families, but its power transmission scales as $\eta = 1-F,$4, which the paper proves to be optimal for typical detector arrangements (Cohen et al., 15 Apr 2026). Diffractive neural networks with flexible detection regions do not fix the desired output field; instead they jointly optimize the phase planes and the detector partition, using

$\eta = 1-F,$5

and the loss

$\eta = 1-F,$6

to expose an efficiency–crosstalk tradeoff (Bearne et al., 27 Aug 2025). This is directly relevant to photon-limited modal receivers because it treats detector segmentation itself as a design variable.

Finally, MPLC-based unambiguous discrimination of non-orthogonal spatial states shows that a passive optical network can act as a simultaneous generalized measurement for overlapping hypotheses (Goel et al., 2022). A plausible implication is that future QPMS receivers may combine nonlinear mode-selective conversion for temporal or spatiotemporal discrimination with linear multiport spatial networks for orthogonalization, demultiplexing, or reject-port generation.

5. LIDAR estimation tasks and receiver logic

The ranging literature closest to QPMS treats lidar not as ordinary direct detection but as a mode-discrimination problem. Quantum target ranging formulates the task as $\eta = 1-F,$7-ary hypothesis testing over range bins,

$\eta = 1-F,$8

so that one slot contains reflected signal plus background and all others contain only background (Ortolano et al., 2024). For these symmetric hypotheses, the asymptotic exponent is

$\eta = 1-F,$9

which satisfies $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$0; the paper therefore concludes that ranging is asymptotically easier than target detection (Ortolano et al., 2024). The practically emphasized receiver is phase-insensitive photon counting, with the decision statistic

$F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$1

for signal-idler count vectors across copies (Ortolano et al., 2024). This is already mode-resolved logic, with the “which range bin?” question functioning as a sorted-mode question.

Joint range and velocity estimation with displaced squeezed light is formulated in an explicitly modal way. The transmitted state is a product of displaced squeezed states over temporal Hermite–Gaussian modes,

$F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$2

and infinitesimal delay and Doppler induce nearest-neighbor temporal-mode mixing,

$F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$3

(Reichert et al., 2023). In the lossless case, the reported mean-squared errors obey

$F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$4

so both range and velocity attain Heisenberg-limited scaling simultaneously under the stated conditions (Reichert et al., 2023). The measurement is standard homodyne detection, but its mode-selective structure is explicit: parameter information is carried by couplings among orthogonal temporal modes.

Quantum-enhanced Doppler lidar makes the same point in the frequency domain. The signal-idler SPDC state is decomposed into Schmidt spectral modes,

$F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$5

and the optimal lossless measurement is frequency-resolved photon counting (Reichert et al., 2022). This does not itself constitute QPMS hardware, but it defines a clear receiver target: a mode sorter that can resolve the relevant spectral or Schmidt-mode structure without discarding the information carried by neighboring-mode redistribution under Doppler shift.

Across these three lidar papers, the recurring theme is that the useful receiver is already mode-specific. QPMS LIDAR can therefore be read as an attempt to realize this mode specificity physically, by replacing purely digital or coarse-bin discrimination with optical mode sorting before detection.

6. Cloud thermodynamic-phase calibration and the explicit QPMS LIDAR proposal

The most explicit QPMS LIDAR paper proposes a dual-lidar architecture for detecting isolated specular reflection from clouds in order to calibrate cloud thermodynamic-phase retrieval (Murchie et al., 22 Sep 2025). The motivation is that horizontally orientated ice crystals can produce high backscatter and low depolarization, which can cause ice clouds to resemble liquid clouds in conventional near-nadir phase-sector logic (Murchie et al., 22 Sep 2025). The proposed remedy is a second, near-concurrent lidar channel that is intentionally biased toward the specular contribution.

In this proposal, the QPMS channel uses SFG in a $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$6 waveguide. The signal interrogates the atmosphere at $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$7 nm, a strong pump is also at $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$8 nm, and the idler is detected at $F=\left|\bra{\psi_i}\psi_{j\ne i}\rangle\right|^2$9 nm (Murchie et al., 22 Sep 2025). The temporal-mode basis is Hermite–Gaussian; the QPMS signal is placed in TM(3), while the conventional lidar specular return is modeled in TM(0) (Murchie et al., 22 Sep 2025). The mode-selective SFG process is written as

$$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$0

and, after Schmidt decomposition,

$$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$1

(Murchie et al., 22 Sep 2025). The numerical feasibility study assumes strong preference for TM(3), with $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$2, $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$3, $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$4, and all others zero (Murchie et al., 22 Sep 2025).

The paper’s operational metric is the strictly standardized mean difference,

$$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$5

with feasibility assessed at $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$6 (Murchie et al., 22 Sep 2025). Solar background is treated as multimode thermal light; with the stated $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$7 nm, $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$8 ps, and bandwidth parameters, the total mean solar background is approximately $$\begin{split} G_{rs}(t,t')=\int_{-\infty}^\infty\mathrm{d}t''\big[G^{(2)}_{rs}(t,t'')G^{(1)}_{ss}(t'',t') +e^{i\theta}G^{(2)}_{rr}(t,t'')G^{(1)}_{rs}(t'',t')\big], \end{split}$$9, distributed across $s$0 HG modes (Murchie et al., 22 Sep 2025). The chosen pulse width $s$1 ps is justified because atmospheric dispersion is mild enough at that scale that, after compensation of first- and second-order terms, the original temporal-mode structure is largely retained (Murchie et al., 22 Sep 2025).

A second central idea in the paper is deliberate low-power operation. The claim is that if the QPMS signal is kept weak, then only the strongest and most directional returns remain detectable, which biases the observed return toward specular reflection rather than Lambertian scattering (Murchie et al., 22 Sep 2025). Using nominal values $s$2, $s$3 mm, and $s$4 nm, the far-field specular-to-Lambertian ratio is estimated as approximately $s$5 (Murchie et al., 22 Sep 2025). The authors therefore present QPMS not as a replacement for conventional cloud lidar, but as an auxiliary calibration channel whose selective detection of specular singly scattered return can improve interpretation of the conventional $s$6 observations.

The feasibility conclusion is explicitly cautious. The paper says the concept could plausibly detect isolated specular backscatter from high-altitude clouds under favorable conditions, but it also identifies several limits: reflector size, contamination from conventional-lidar multiple scattering, mode degradation, the simplicity of the planar-mirror reflector model, and the omission of polarization (Murchie et al., 22 Sep 2025). The proposal is therefore a conceptual study, not an operational cloud-remote-sensing demonstration.

7. Limitations, tradeoffs, and unresolved engineering questions

The current QPMS literature is strongest on receiver primitives and weakest on fully fielded lidar systems. Several limitations recur across the papers.

First, many of the most distinctive devices are not unitary lossless sorters. The multi-output quantum pulse gate has non-unity conversion efficiency and therefore an inconclusive POVM element (Serino et al., 2024). The spatiotemporal QPMS sorter is a single-channel programmable projector rather than a parallel many-output sorter, and its laboratory implementation is constrained by waveshaper response time $s$7 ms, spatial-light-modulator response time $s$8 ms, and roughly $s$9 s per pump-signal pair in the reported measurement loop (Garikapati et al., 2022). These facts directly limit adaptive or high-frame-rate lidar use.

Second, spatial subsystems remain sensitive to matching conditions and dimensionality. The FRFT radial sorter requires the beam-waist condition

$r$0

and depends on fixed or separately known $r$1 for pure radial discrimination (Zhou et al., 2017). The multimode-fiber arbitrary-basis sorter is programmable, but its sorting ability falls rapidly with mode number and its real implementation is phase-only rather than fully unitary (Defienne et al., 2020). The single-plane spatial sorter offers analytic simplicity, but its power transmission coefficient scales as $r$2, which is a severe penalty in photon-starved receivers (Cohen et al., 15 Apr 2026).

Third, scaling and readout constraints are unresolved in the most advanced time-frequency devices. The multi-output quantum pulse gate demonstrates $r$3 and $r$4 operation, but practical single-shot readout is limited by spectrograph resolution; the fast time-of-flight spectrograph has $r$5 GHz resolution, whereas the phase-matching peak width is approximately $r$6 GHz (Serino et al., 2024). The paper therefore identifies spectral bandwidth, synchronization, and spectrographic resolution as the primary obstacles to higher-dimensional scaling (Serino et al., 2024).

Fourth, most lidar-specific environmental impairments remain untreated. The cloud-calibration proposal neglects atmospheric turbulence and uses a highly simplified reflector model (Murchie et al., 22 Sep 2025). Quantum target ranging does not include sorter loss, modal nonorthogonality, or realistic idler-storage imperfections (Ortolano et al., 2024). Quantum-enhanced Doppler lidar provides a loss analysis, but it does not discuss parametric mode-sorter imperfections or atmospheric channel distortion (Reichert et al., 2022). This suggests that the present literature is still primarily architectural and laboratory-oriented.

Finally, there is a persistent tradeoff between universality and efficiency. The arbitrary-basis multimode-fiber sorter is flexible but incurs loss because only a phase-only diagonal operator is realized (Defienne et al., 2020). Flexible-region diffractive neural sorters improve the efficiency–crosstalk frontier but remain passive linear optics rather than nonlinear quantum receivers (Bearne et al., 27 Aug 2025). Conversely, nonlinear QPMS receivers provide strong selectivity and background rejection, but at the cost of pump synchronization, conversion loss, and—in present demonstrations—sequential rather than parallel readout (Garikapati et al., 2022).

The present state of the field therefore supports a narrow but technically precise conclusion. QPMS LIDAR is already well defined at the level of modal measurement theory and receiver primitives: mode-selective SFG, temporal-mode interferometry, programmable time-frequency projection, radial and arbitrary-basis spatial sorting, and multiport generalized measurements have all been demonstrated in adjacent settings [(Reddy et al., 2014); (Serino et al., 2024); (Garikapati et al., 2022); (Zhou et al., 2017); (Defienne et al., 2020); (Goel et al., 2022)]. What remains unresolved is the end-to-end lidar problem: photon-efficient packaging, parallelism, synchronization under unknown delay, atmospheric robustness, detector integration, and quantitative performance in realistic ranging or remote-sensing scenes.