Quantum-Enhanced Sensing Methods & Applications

• Quantum-enhanced sensing is defined as the use of nonclassical resources, such as spin squeezing and hyperentanglement, to overcome classical measurement limits.
• It employs diverse protocols—including entanglement-assisted interferometry, bosonic interferometers, and non-Hermitian techniques—to achieve improved signal-to-noise ratios and measurement accuracy.
• Practical implementations in atomic, photonic, and hybrid platforms demonstrate actionable benefits like sub-SQL operation and near-Heisenberg scaling in sensitivity.

Searching arXiv for the papers on arXiv and closely related work on quantum-enhanced sensing. Quantum-enhanced sensing denotes sensing protocols in which nonclassical resources reduce estimation error, lower detection thresholds, or improve search complexity beyond classical or shot-noise-limited baselines. In the literature surveyed here, the operative resources include spin squeezing, hyperentanglement, bosonic superpositions, interaction-based readout, hybrid-spin amplification and deamplification, criticality, non-Hermitian spectral structure, information scrambling, and quantum algorithms. The resulting tasks range from phase and field estimation in atomic and photonic interferometers to weak-target detection, broadband AC-signal search, and post-hoc learning of many properties of a classical field from a single quantum measurement record (Mao et al., 2022, Walborn et al., 2017, McCormick et al., 2018, Jiang et al., 2023, Allen et al., 13 Jan 2025, Cotler et al., 19 Feb 2026).

1. Metrological foundations and figures of merit

The canonical benchmark is the standard quantum limit (SQL), while the asymptotic aspirational benchmark is Heisenberg scaling. In the unitary pure-state setting, the Cramér–Rao bound is written as

$\delta\theta \ge \frac{1}{\sqrt{\nu F(\theta)}},$

with Fisher information $F(\theta)$, repetition number $\nu$, and quantum Fisher information (QFI) $\mathcal F(\theta)$ obtained by optimizing over measurements; for pure states under unitary evolution, $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$ (Walborn et al., 2017). Mixed-state analyses also appear centrally in noisy-target and local-many-body sensing, where QFI is evaluated from the spectrum of the output density operator rather than directly from a variance formula (Lee et al., 2020, Mishra et al., 2020).

In experimental quantum sensing, the abstract Fisher-information language is often converted into platform-specific gain metrics. In spin-squeezing-based interferometry on optical transitions, the Wineland parameter

$$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$

is directly related to the SQL through

$$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$

so negative values in dB indicate sub-SQL operation (Franke et al., 2023). In spin-1 condensate nonlinear interferometry, gain is reported as

$$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$

with both a two-mode SQL $(\Delta\phi)_{\rm SQL}=1/\sqrt N$ and a three-mode SQL $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$ depending on the interferometric structure (Mao et al., 2022).

The same field also uses operational SNR criteria. In Fourier-domain interferometric sensing with $F(\theta)$0-photon probes, the detected coincidence probability in the small-modulation regime yields a PSD of the form

$F(\theta)$1

This makes explicit that the spectral line at $F(\theta)$2 is unchanged while the noise floor scales as $F(\theta)$3, giving

$F(\theta)$4

and therefore a $F(\theta)$5 dB improvement for the $F(\theta)$6 versus $F(\theta)$7 comparison (Dalidet et al., 18 Feb 2026). This framing is important because quantum enhancement need not appear as signal amplification; it can appear as spectral-noise suppression.

2. Entanglement-assisted interferometry and interaction-based readout

A central route to quantum-enhanced sensing uses entangled many-body probe states together with readout protocols that preserve the metrological gain in the presence of realistic detection noise. In a spin-1 $F(\theta)$8 Bose–Einstein condensate initialized in the polar state $F(\theta)$9, spin-exchange dynamics near $\nu$0 generate a spin-nematic squeezed vacuum governed by

$\nu$1

The squeezing is quantified by

$\nu$2

with best observed squeezing $\nu$3 dB, improving to $\nu$4 dB after subtraction of detection noise. The key readout innovation is an echo protocol: nonlinear splitting, a $\nu$5 state flip around $\nu$6 that exchanges squeezing and anti-squeezing axes, and nonlinear recombination. For a small-angle RF Rabi rotation, this yields $\nu$7 dB relative to the three-mode SQL, equivalent to $\nu$8 dB beyond the two-mode SQL for $\nu$9 atoms. In a Ramsey interferometer it yields $\mathcal F(\theta)$0 dB over SQL and an extrapolated absolute near-resonant microwave-field sensitivity of $\mathcal F(\theta)$1 at a probe volume of $\mathcal F(\theta)$2 (Mao et al., 2022).

An optical-transition implementation on trapped-ion chains realizes a related but microscopically distinct form of collective enhancement. In 1D chains of up to $\mathcal F(\theta)$3 $\mathcal F(\theta)$4 ions, a power-law transverse-field Ising model operated in the $\mathcal F(\theta)$5 regime becomes an effective XX exchange model that reproduces the collective behavior associated with one-axis twisting (OAT). The dynamics preserve total transverse magnetization more effectively than a corresponding finite-range Ising evolution, suppress the growth of finite-$\mathcal F(\theta)$6 spin-wave excitations, generate a Wineland parameter of $\mathcal F(\theta)$7 dB for $\mathcal F(\theta)$8, and reduce Ramsey measurement uncertainty by $\mathcal F(\theta)$9 dB below the SQL for $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$0 (Franke et al., 2023). The same experiment also observes non-Gaussian multi-headed cat states in the Husimi $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$1-distribution at longer times.

Hyperentanglement supplies a photonic realization in which multiple degrees of freedom contribute independently to the Fisher information. In the mirror-tilt protocol based on photon pairs entangled in polarization and spatial modes, the single-photon and two-photon encoding unitaries are

$\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$2

The corresponding QFI for a hyperentangled pair,

$\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$3

contains contributions from spatial spread, beam displacement, and spatial covariance. In the maximally correlated case this becomes

$\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$4

which is the two-photon Heisenberg enhancement. Experimentally, a simple binary polarization projection saturates the QFI in the small-angle regime and yields sub-shot-noise precision for large beam displacement $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$5 mm (Walborn et al., 2017).

3. Bosonic, photonic, and spatially parallel implementations

Bosonic interferometers exploit large Hilbert spaces rather than large qubit registers. In a trapped-ion mechanical oscillator, Ramsey interferometry between $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$6 and $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$7 uses the motional superposition

$\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$8

which acquires a relative phase $\mathcal F(\theta)=4\langle \Delta \hat H^2\rangle$9 under free evolution, producing

$$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$0

The ideal phase sensitivity is therefore $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$1, compared with the coherent-state benchmark $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$2. Experimentally, number states were generated up to $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$3 and superpositions up to $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$4; the best observed sensing performance occurred at $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$5, with $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$6 dB better sensitivity than an ideal classical interferometer with the same average occupation number, and frequency tracking of the axial mode of a single $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$7 ion reached an Allan deviation $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$8 after about $$\xi^2 = \min_{\mathbf n_\perp} \frac{N\langle(\Delta \hat S_{\mathbf n_\perp})^2\rangle}{|\langle \hat{\mathbf S}\rangle|^2}$$9 s (McCormick et al., 2018).

A single photonic or bosonic mode can also be used as a sensor via cat-state coherence. For the Hamiltonian $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$0, free evolution induces a phase-space rotation $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$1. Using the amplitude cat state

$$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$2

the protocol converts the rotation into qubit-readout fringes through a Ramsey sequence and a conditional parity gate. In the large-cat, small-angle regime,

$$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$3

and the signal-to-noise ratio

$$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$4

satisfies $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$5 at the optimal working point, i.e. Heisenberg-limit-like scaling in the ideal lossless case. With dissipation, the same work finds an optimum rather than indefinite improvement; for $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$6, the maximal reported value is $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$7 at $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$8 (Zheng et al., 30 Mar 2025).

Optical platforms also show that quantum advantage can survive substantial loss and can be distributed across sensor arrays. In plasmonic surface-plasmon-resonance sensing, bright twin beams from four-wave mixing reduce the intensity-difference noise below the shot-noise level and improve refractive-index sensitivity from $$\xi^2=\left(\frac{\Delta\phi}{\Delta\phi_{\rm SQL}}\right)^2, \qquad \Delta\phi_{\rm SQL}=\frac{1}{\sqrt N},$$9 to $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$0, corresponding to a $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$1 enhancement; the same work reports $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$2 dB source squeezing, reduced to $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$3 dB after the sensor and other losses (Dowran et al., 2018). In a four-sensor quadrant plasmonic array illuminated by multi-spatial-mode twin beams, independent probe–conjugate spatial subregions permit simultaneous readout of local refractive-index changes with a quantum sensitivity enhancement in the range of $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$4 to $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$5 over the classical configuration (Dowran et al., 2023). In fiber interferometry, the spectral-domain viewpoint isolates a different operational mechanism: identical $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$6 Hz modulation peaks for single-photon and two-photon interference, but a $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$7 dB lower quantum noise floor, with the two-photon signal remaining resolvable when the single-photon signal is buried in the spectral background (Dalidet et al., 18 Feb 2026).

4. Noise-robust transduction, amplification, and sensing in noisy backgrounds

Several recent protocols shift the emphasis from state preparation alone to preprocessing of the signal before final detection. In a warm-vapor hybrid sensor containing isotopically enriched $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$8 and polarized $$-20\log_{10}\!\left[\frac{\Delta\phi}{(\Delta\phi)_{\rm SQL}}\right],$$9, rapid spin-exchange collisions generate coupled alkali and noble-gas dynamics with effective coupling $(\Delta\phi)_{\rm SQL}=1/\sqrt N$0 Hz. Because the alkali response is broad ($(\Delta\phi)_{\rm SQL}=1/\sqrt N$1 kHz) and the noble-gas response is narrow ($(\Delta\phi)_{\rm SQL}=1/\sqrt N$2 mHz), their interference produces a Fano resonance

$(\Delta\phi)_{\rm SQL}=1/\sqrt N$3

Near resonance, the effective-field amplification factor

$(\Delta\phi)_{\rm SQL}=1/\sqrt N$4

is essentially equal to the Fano parameter, $(\Delta\phi)_{\rm SQL}=1/\sqrt N$5; experimentally $(\Delta\phi)_{\rm SQL}=1/\sqrt N$6, giving pre-amplification of more than two orders of magnitude. The same platform demonstrates magnetic-field measurement about $(\Delta\phi)_{\rm SQL}=1/\sqrt N$7 dB below the photon-shot-noise level of the $(\Delta\phi)_{\rm SQL}=1/\sqrt N$8 magnetometer, a magnetic sensitivity about $(\Delta\phi)_{\rm SQL}=1/\sqrt N$9, and magnetic-background suppression of about $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$0 dB in deamplification mode (Jiang et al., 2023). This directly addresses the practical regime in which detector noise exceeds the intrinsic sensor sensitivity.

A complementary generalization appears in the bridge between quantum-enhanced sensing and quantum illumination. In the weak-target limit, a target of reflectivity $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$1 is modeled by

$(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$2

and the resulting QFI at $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$3 matches the QFI of phase sensing in a $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$4 interferometer. Under a fixed total input energy constraint, optimized $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$5-photon entangled states outperform both TMSV and separable coherent states, and the paper connects the target sensitivity to a practical photon-number-difference measurement

$(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$6

and to an SNR that functions as an effective error exponent for target detection. A striking reported result is that increasing thermal noise can improve both target sensitivity and SNR for optimized entangled states in the weak-target regime (Lee et al., 2020). This does not state that thermal noise is generically beneficial; it states that in the specific model considered, the correlated structure of the entangled probe can turn thermal contributions into a net advantage.

A more expansive sensing architecture is Quantum Signal Learning (QSL), which treats a classical field as inducing an unknown displacement distribution rather than a single scalar parameter. In Bell QSL, a TMSV resource, passive optics, and static homodyne Bell measurements generate effective samples

$(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$7

so both quadratures are estimated simultaneously with noise suppressed below the vacuum level. The protocol is explicitly designed for post-hoc estimation of many functionals of the displacement distribution from the same dataset, and the sample complexity for a property kernel $(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$8 is bounded by

$(\Delta\phi)_{\rm SQL}=1/(2\sqrt N)$9

The same work proves worst-case exponential separations from entanglement-free strategies for matched filtering and other classical-field tasks, and practical speedups over homodyne and heterodyne baselines (Cotler et al., 19 Feb 2026).

5. Criticality, localization, driven many-body dynamics, and non-Hermitian sensors

Quantum criticality has long been identified as a metrological resource, but the recent literature broadens this notion beyond equilibrium ground states. In the Aubry–André–Harper lattice, the single-particle Hamiltonian

$F(\theta)$00

has an energy-independent localization transition at $F(\theta)$01. Near the transition, the QFI reaches essentially Heisenberg scaling, with $F(\theta)$02 in the single-particle case and $F(\theta)$03 at half filling; even with $F(\theta)$04, the reported scaling is $F(\theta)$05. Experimentally meaningful observables do not always saturate this bound but can still be super-SQL: $F(\theta)$06 for the charge-density-wave imbalance, while dynamical quench protocols yield $F(\theta)$07 and $F(\theta)$08 in the transient regime (Sahoo et al., 2023).

When only part of a many-body system is accessible, equilibrium critical metrology degrades. For a block of $F(\theta)$09 spins in the ground state of a driven $F(\theta)$10 chain, the local QFI scales only as $F(\theta)$11 with fitted exponents $F(\theta)$12, $F(\theta)$13, and $F(\theta)$14 for $F(\theta)$15, $F(\theta)$16, and $F(\theta)$17, respectively. Periodic driving alters this picture by replacing ground-state sensing with local steady-state sensing governed by Floquet resonances. The steady-state QFI satisfies $F(\theta)$18 at $F(\theta)$19, while for lower frequencies $F(\theta)$20 the reported scaling is super-Heisenberg, $F(\theta)$21 with $F(\theta)$22. The enhancement is traced to closure of the Floquet quasienergy gap, the driven analogue of equilibrium gap closing at a critical point (Mishra et al., 2020).

A non-equilibrium realization on superconducting hardware uses Stark–Wannier localization in a $F(\theta)$23-qubit chain with exchange coupling $F(\theta)$24. The unknown parameter is the linear gradient field $F(\theta)$25. Projective computational-basis measurements at multiple evolution times are combined through a Bayesian estimator,

$F(\theta)$26

and the resulting reciprocal variance scales as $F(\theta)$27 with $F(\theta)$28 for $F(\theta)$29 time points and $F(\theta)$30 for $F(\theta)$31, i.e. near-Heisenberg-limited precision in time. The extended phase outperforms the localized phase, and the transition is identified numerically near $F(\theta)$32 for single excitation and $F(\theta)$33 for double excitation (Li et al., 20 Aug 2025).

Non-Hermitian and non-unitary platforms add another route to enhanced susceptibility. In a photonic non-unitary quantum walk, transient-time dynamics already exhibit critical sensitivity associated with topological point-gap and line-gap closings. Experimentally, the maximum CFI scales as $F(\theta)$34 with $F(\theta)$35 near the point-gap transition and $F(\theta)$36 near the line-gap transition, whereas away from criticality the exponents drop to $F(\theta)$37 and $F(\theta)$38, respectively (Xiao et al., 19 Jun 2025). A time-modulated non-Hermitian qubit shows a related but more explicitly dynamical effect: eigenvalue-based sensing using the splitting $F(\theta)$39 reaches a $F(\theta)$40-fold improvement over a conventional Hermitian sensor, while eigenstate-based sensing using time-dependent instantaneous-eigenstate populations reaches up to $F(\theta)$41-fold enhancement and can exhibit divergent susceptibility even when the trajectory is not close to an exceptional point (Wu et al., 20 Mar 2025).

6. Information scrambling, quantum computation, and generalized sensing tasks

A recent conceptual shift is the use of dynamical complexity itself as the sensing resource. Butterfly metrology prepares a coherent superposition of an unscrambled branch and a scrambled branch by applying forward evolution $F(\theta)$42, a local butterfly operator $F(\theta)$43, backward evolution $F(\theta)$44, phase encoding $F(\theta)$45, and then a second forward evolution. In the local-control version, the butterfly state has the schematic form

$F(\theta)$46

and the small-$F(\theta)$47 sensitivity is

$F(\theta)$48

For a fully scrambled, Haar-random state this gives $F(\theta)$49, i.e. Heisenberg scaling up to normalization conventions. The same work makes the dependence on scrambling explicit through local OTOCs and operator space-time volumes, so the metrological gain is tied directly to operator spreading (Kobrin et al., 2024). An experimental implementation on a superconducting processor with $F(\theta)$50 qubits observes increasing phase-response slopes $F(\theta)$51, $F(\theta)$52, and $F(\theta)$53, OTOC decay, GME concurrence peaking around $F(\theta)$54 ns for $F(\theta)$55, and sensitivity beyond the SQL with normalized scaling linear in $F(\theta)$56, consistent with a factor-of-two of the Heisenberg limit (Hu et al., 30 Jan 2026).

Quantum computation can also change the complexity class of a sensing task. For AC sensing of a weak oscillating field

$F(\theta)$57

with unknown amplitude, frequency, and phase, quantum search sensing partitions the frequency band into

$F(\theta)$58

bins, digitizes the analog response into a sensing oracle $F(\theta)$59, and applies Grover-style amplitude amplification. The resulting sensing time satisfies

$F(\theta)$60

while the Grover–Heisenberg lower bound is

$F(\theta)$61

The same work proves that protocols based only on QFI, finite-lifetime quantum memory, or classical modulation obey strictly weaker bounds for this broadband detection problem (Allen et al., 13 Jan 2025).

Generalized target detection can likewise be recast as quantum-enhanced sensing. The phase-sensing/target-sensing equivalence established through QFI shows that weak-reflectivity target detection can be analyzed with metrological tools and then connected to practical discrimination through SNR and error exponents (Lee et al., 2020). QSL extends this logic further by replacing single-parameter estimation with property learning over an unknown displacement distribution, making informational completeness and post-hoc reuse of data central rather than incidental (Cotler et al., 19 Feb 2026).

Across these disparate formulations, several recurrent misconceptions are corrected by the recent literature. Quantum enhancement does not always mean a larger signal peak; in Fourier-domain interferometry it can mean a lower spectral noise floor (Dalidet et al., 18 Feb 2026). It does not always require ultra-low-noise final detectors; interaction-based readout and hybrid-medium amplification can move the burden of sensitivity enhancement upstream of the detector (Mao et al., 2022, Jiang et al., 2023). It is not restricted to entangled probe states in the narrow sense; scrambling-based protocols, Groverized search, and QSL derive their gain from operator growth, coherent query complexity, or informationally complete sub-vacuum-noise datasets (Kobrin et al., 2024, Allen et al., 13 Jan 2025, Cotler et al., 19 Feb 2026). At the same time, the literature is equally clear that realized gains remain contingent on loss, decoherence, control infidelity, finite-time operation, and measurement nonoptimality, which is why many experimentally observed advantages remain below their ideal asymptotic limits (McCormick et al., 2018, Franke et al., 2023, Li et al., 20 Aug 2025, Mishra et al., 2020).