---
title: Amplitude-Quadrature Squeezing in Quantum Optics
url: https://www.emergentmind.com/topics/amplitude-quadrature-squeezing
type: topic
---

# Amplitude-Quadrature Squeezing in Quantum Optics

Searching arXiv for recent papers on amplitude/quadrature squeezing across relevant platforms.
Amplitude-quadrature squeezing is the reduction of fluctuations in the amplitude quadrature of a bosonic mode below the shot-noise or vacuum level, with a compensating increase in the conjugate quadrature required by the uncertainty relation. For a single mode with annihilation operator \(\hat a\), the canonical quadratures are commonly written as \(\hat X = (\hat a+\hat a^\dagger)/\sqrt{2}\) and \(\hat P = (\hat a-\hat a^\dagger)/(i\sqrt{2})\), or equivalently \(\hat X_1\) and \(\hat X_2\) in interferometric notation [1602.03233][2408.16688]. In coherent states the two quadratures have equal variance, whereas a squeezed state generated by \(\hat S(r,\phi)=\exp\{\tfrac{r}{2}(e^{-i2\phi}\hat a^2-e^{i2\phi}\hat a^{\dagger 2})\}\) redistributes noise so that one rotated quadrature has variance proportional to \(e^{-2r}\) and the orthogonal quadrature has variance proportional to \(e^{+2r}\) [1602.03233][2408.16688]. In this sense, amplitude-quadrature squeezing denotes either direct suppression of \(\hat X\) or \(\hat X_1\), or a frequency-dependent situation in which the optimally squeezed quadrature remains close to the amplitude axis over the band of interest [1602.03233]. The concept has become central across gravitational-wave interferometry, dual-comb spectroscopy, semiconductor lasers, integrated nonlinear photonics, cavity optomechanics, atomic media, and magnonic systems, where the experimentally relevant observable is often intensity noise, radiation-pressure back-action, or a measured position-like quadrature [2008.08094][2408.16688][2309.09703].

## 1. Canonical formulation and metrological meaning

For a single bosonic mode, amplitude-quadrature squeezing is defined by a variance below the vacuum or shot-noise reference in the amplitude quadrature. In the normalization \(\hat X=(\hat a+\hat a^\dagger)/\sqrt{2}\), \(\hat P=(\hat a-\hat a^\dagger)/(i\sqrt{2})\), the vacuum has \(\mathrm{Var}(\hat X)=\mathrm{Var}(\hat P)=1/2\), while in shot-noise-normalized conventions used in several experiments the coherent-state variance is set to \(1\) [2408.16688][2309.09703]. For a pure squeezed vacuum aligned to angle \(\phi\), the rotated quadrature \(\hat X_\phi=\hat X\cos\phi+\hat P\sin\phi\) has variance \(\tfrac12 e^{-2r}\) and the orthogonal quadrature has variance \(\tfrac12 e^{+2r}\) [2408.16688]. In interferometric notation, the same content is written as \(\hat X_1=(\hat a+\hat a^\dagger)/\sqrt{2}\) and \(\hat X_2=(\hat a-\hat a^\dagger)/(i\sqrt{2})\), with amplitude-quadrature squeezing corresponding to \(V(\hat X_1)<1\) in shot-noise units [1602.03233].

For bright beams, amplitude-quadrature squeezing is directly connected to intensity noise. When \(|\alpha|\gg 1\), the photon number obeys \(\hat n \approx |\alpha|^2+\sqrt{2}|\alpha|\,\delta \hat X\), so direct-detection intensity fluctuations are linearly proportional to amplitude-quadrature fluctuations [2408.16688]. This is why amplitude squeezing is the relevant resource in intensity-dominated measurements such as direct photodetection, relative-intensity-noise suppression, and large-delay dual-comb interferograms [2408.16688]. In gravitational-wave interferometers, the same quadrature has a different operational meaning: amplitude fluctuations drive radiation-pressure noise on the test masses, while phase fluctuations dominate shot noise, so control of the amplitude quadrature is decisive below the interferometer’s scale frequency [1602.03233][2008.08094].

The conversion between variance and decibel units follows directly from the chosen normalization. In SNL-normalized units, a squeezed variance \(V\) is reported as \(10\log_{10}(V)\), so negative values denote squeezing [2309.09703]. For ideal squeezing \(V=e^{-2r}\), the corresponding reduction is \(-8.686\,r\) dB [2408.16688]. Loss degrades the observable squeezing according to \(V_{\mathrm{obs}}=\eta V_{\mathrm{in}}+(1-\eta)\) in SNL units, which makes efficiency a universal constraint across optical, semiconductor, and integrated implementations [2408.16688][2502.17337][1906.09749].

## 2. Frequency-dependent amplitude squeezing and quadrature rotation

Amplitude-quadrature squeezing need not remain aligned to a fixed quadrature. In cavity optomechanics, the coexistence of \(\delta \hat a_{\rm in}\) and \(\delta \hat a_{\rm in}^\dagger\) pathways in the output field generates ponderomotive correlations that rotate the optimal squeezing angle across frequency [1602.03233]. In the optomechanical cavity studied for gravitational-wave applications, the output quadrature spectrum can be written as
\[
S_\theta(\omega)=\frac{S_X(\omega)+S_Y(\omega)}{2}
+\frac{S_X(\omega)-S_Y(\omega)}{2}\cos(2\theta)
+S_{XY}(\omega)\sin(2\theta),
\]
with minimizing angle
\[
\theta_{\min}(\omega)=\frac{\pi}{2}+\frac{1}{2}\arctan\!\left[\frac{2S_{XY}(\omega)}{S_X(\omega)-S_Y(\omega)}\right].
\]
This makes the amplitude–phase cross-correlation \(S_{XY}\) the direct origin of frequency-dependent quadrature rotation [1602.03233].

In the acoustic band relevant to gravitational-wave detectors, an optomechanical cavity with \(\omega_m/2\pi=150\) Hz, \(Q_m=5\times 10^6\), \(m=0.5\) kg, \(T=3\) mK, \(\kappa=2\pi\times 0.5\) MHz, and \(P_{\rm in}=20\) W produces squeezing concentrated around the effective mechanical resonance \(\omega_{\rm eff}\) set by the optical spring [1602.03233]. At zero detuning, the optimal squeezed angle varies from about \(\pi/12\) at DC to about \(-\pi/6\) at \(300\) Hz, an overall rotation of \(\sim \pi/4\), so the output is closer to amplitude squeezing at low frequency and closer to phase squeezing at higher frequency [1602.03233]. For \(\Delta=\pm 0.5\kappa\), slightly larger rotations occur, while very large \(|\Delta|\) weaken the correlations and largely remove the advantage [1602.03233]. The paper caps the squeeze factor at \(10\) dB to compare fairly with traditional sources and finds 3, 6, and 9 dB squeezing regions near, but not exactly at, \(\omega_{\rm eff}\) [1602.03233].

A closely related phenomenon was measured in hot rubidium vapor using bichromatic homodyne detection. There, nondegenerate four-wave mixing generated broadband quadrature squeezing in bands separated by more than \(6\) GHz, and the measured noise ellipse rotated by approximately \(\pi/2\) across a squeezing spectrum of \(\sigma \approx 2\pi\times 40\) MHz [1609.03196]. An all-atomic configuration based on polarization self-rotation and electromagnetically induced transparency showed the same underlying principle: broad, symmetric EIT windows mainly attenuate squeezing, while narrower and asymmetric windows produce observable squeeze-angle rotation through the phase
\[
\phi(\Omega)=\tfrac12\big(\Theta_+(\Omega)+\Theta_-(\Omega)\big)
\]
imparted to the sidebands [1204.3967]. This establishes frequency-dependent amplitude squeezing as a dispersive resource rather than only a static reduction of \(\hat X\)-noise.

## 3. Generation mechanisms across physical platforms

In Kerr-fiber frequency combs, amplitude-quadrature squeezing is produced by the \(\chi^{(3)}\) Kerr Hamiltonian \(\hat H_{\mathrm{Kerr}}=\hbar\kappa\,\hat a^\dagger\hat a^\dagger\hat a\hat a\), together with a displacement that aligns the Kerr-noise ellipse with the direct-detection amplitude axis [2408.16688]. In the reported experiment, \(1\) GHz repetition-rate femtosecond combs centered at about \(1563\) nm propagate through a \(7\) m PM-HNLF in an unbalanced interferometer. The strong arm acquires Kerr nonlinearity, then recombines with a weak auxiliary at about \(100{:}1\) and relative phase near \(90^\circ\) to realize amplitude squeezing [2408.16688]. RF-domain measurements showed \(3.8\) dB squeezing and \(4.0\) dB anti-squeezing in a \(45\)–\(50\) MHz band, more than \(3\) dB from \(10\) to \(100\) MHz, and about \(2\) dB out to \(500\) MHz, across an optical comb spanning about \(2.5\) THz with about \(2500\) teeth spaced by \(1\) GHz [2408.16688].

Semiconductor lasers provide a distinct mechanism based on carrier regulation rather than optical parametric conversion. In electrically driven quantum-dot DFB lasers at \(1.31\,\mu\)m and \(20^\circ\)C, amplitude-quadrature squeezing was observed from \(3\) to \(12\) GHz, with a maximum reduction of \(0.9\pm 0.1\) dB below shot noise near \(8\) GHz [2309.09703]. The underlying model combines quiet-current injection, Coulomb-regulated carrier flow, and QD-specific small depletion capacitance, giving a squeezing bandwidth
\[
B=\frac{1}{2\pi(\tau_{te}+\tau_p)},\qquad
\tau_{te}=\frac{k_B T\,C_{\mathrm{dep}}}{eI}.
\]
The paper argues that QD lasers can reach tens of GHz at room temperature because \(C_{\mathrm{dep}}\) can be as low as \(\sim 3.5\) pF and \(\tau_p\) is a few picoseconds [2309.09703]. A later fully quantum treatment of quantum-well lasers extended this picture to frequency-dependent and hidden squeezing, showing that low-frequency amplitude squeezing appears for pump parameter \(a\gtrsim 4\), does not exceed about \(5\) dB in the examined regime, and becomes frequency-rotated at finite \(\omega\) by the linewidth-enhancement factor \(\alpha_H\) [2606.26266].

Integrated Kerr photonics realizes the same quadrature resource in chip-scale microresonators. In a silicon-nitride photonic crystal ring, degenerate dual-pump spontaneous four-wave mixing implements an effective degenerate parametric amplifier with Hamiltonian
\[
H=\frac{i\hbar\chi}{2}(a^{\dagger 2}-a^2),
\]
and selective nano-corrugation splits the \(X_{\pm2}\) resonances to suppress parasitic single-pump SFWM and Bragg-scattering FWM [2502.17337]. With intrinsic loss \(\kappa_0\approx 2\pi\times 55\) MHz, outcoupling efficiency \(\eta\approx 0.9\), total linewidth \(\kappa\approx 2\pi\times 550\) MHz, and total on-chip pump power of about \(33\) mW, the measured spectrum showed \(2.4\) dB squeezing and \(8.3\) dB anti-squeezing at low offset frequency, corresponding to about \(7.8\) dB on-chip squeezing and about \(11.3\) dB intracavity squeezing [2502.17337]. A fiber-coupled PPLN ridge-waveguide module provides an alternative \(\chi^{(2)}\) route: at \(1553.3\) nm with \(330\) mW CW pump, it measured \(-4.0\pm 0.1\) dB squeezing and \(+14.1\pm 0.1\) dB anti-squeezing at \(10\) MHz, with \(-5.7\pm 0.1\) dB inferred at the module output fiber after excluding extrinsic detection losses [1906.09749].

Atomic and hybrid matter platforms also exhibit amplitude-like quadrature squeezing. In hot \(^{87}\)Rb vapor, polarization self-rotation produced low-sideband squeezed vacuum of about \(-1.5\) to \(-2\) dB with anti-squeezing of about \(8\)–\(9\) dB [1204.3967]. In uniaxial antiferromagnets, the pairing term \(a_{\mathbf{k}}b_{-\mathbf{k}}+a_{\mathbf{k}}^\dagger b_{-\mathbf{k}}^\dagger\) generates equilibrium two-mode magnon squeezing; the collective amplitude quadrature satisfies
\[
\Delta X_{\mathbf{k}}^2(T,\mathcal{K}_z)=\frac{2\bar n_{\mathbf{k}}(T)+1}{2}\,e^{-2r_{\mathbf{k}}(T,\mathcal{K}_z)},
\]
so temperature enhances amplitude squeezing while anisotropy suppresses it [2304.07602]. This suggests that “amplitude quadrature” in the broad sense is a unifying concept across optical, mechanical, spin, and magnonic bosonic modes.

## 4. Detection, estimation, and state reconstruction

Balanced homodyne detection remains the standard direct probe of amplitude-quadrature squeezing. With a strong local oscillator, the difference photocurrent is proportional to the selected signal quadrature, so the amplitude quadrature is accessed when the LO phase is aligned to \(\hat X\) or \(\hat X_1\) [2309.09703][1906.09749]. In the QD-laser experiment, a \(90/10\) split created the squeezed signal and strong LO from the same device output, two matched \(20\) GHz balanced photoreceivers measured the difference current, and shot noise was calibrated both by scanning the LO phase under normal pumping and by blocking the LO branch so vacuum entered the signal port; the two SQL calibration procedures agreed, with phase stability of \(\pm 0.08\) dB at \(8\) GHz [2309.09703]. In the fiber-coupled PPLN module, the LO phase was scanned with a phase modulator and the minimum-noise point identified the amplitude quadrature, with shot noise established by LO-only measurements at \(10\) MHz [1906.09749].

When the squeezed bands are separated by frequencies beyond electronics bandwidth, bichromatic homodyne detection replaces the single-frequency LO by two tones placed near the correlated bands. The normalized photocurrent spectrum becomes
\[
S_i(\Omega,\Phi)=e^{+2s}\cos^2\!\big[(\Phi-\theta)/2\big]+e^{-2s}\sin^2\!\big[(\Phi-\theta)/2\big],
\]
so scanning \(\Phi\) directly retrieves both the squeezing strength and the squeezing angle [1609.03196]. This is essential for broadband nondegenerate squeezing because it preserves phase information between widely separated sidebands. The same logic underlies synodyne detection in semiconductor-laser squeezing, where a two-tone LO accesses imaginary parts of the cross-covariance that standard homodyne misses, revealing hidden squeezing below the best real-quadrature value [2606.26266].

Not all estimation strategies require a phase reference. For single-mode Gaussian states, measured Fock-state populations can be fit directly to the squeezed thermal distribution
\[
V_q=\frac12(2\bar n+1)e^{-2r},\qquad
V_p=\frac12(2\bar n+1)e^{+2r},
\]
using a weighted least-squares estimator on photon-number statistics [2111.04923]. Simulations with \(10{,}000\) Fock measurement events produced estimates whose fidelities exceeded \(99.99\%\) for small squeezing \(r<1.0\), and exceeded \(99.9\%\) for \(r=2.5\) [2111.04923]. This provides a route to amplitude-squeezing estimation when homodyne detection is unavailable.

In continuous-measurement platforms, amplitude squeezing can also be generated by the readout itself. In a qubit-based indirect measurement of a harmonic oscillator, repeated measurements of the oscillator quadrature \(I=a+a^\dagger\) produce a squeezed conditional state with variance
\[
(\Delta I)^2=\frac{1}{1+4\phi^2 s},
\]
where \(\phi\) is the effective interaction strength and \(s\) the number of repetitions [1704.04533]. In optomechanical PID-feedback control, homodyne detection of the cavity output phase quadrature yields information about the mechanical rotating-frame amplitude quadrature \(\hat Q\), and the unconditional stationary variance becomes
\[
V_Q=n_{\mathrm{th}}+\frac12-4n_{\mathrm{BA}}\Big(n_{\mathrm{th}}+\frac12\Big)^2
\left[
\frac{\alpha_P}{(1+\alpha_P)(1+\alpha_D)}+\frac{\alpha_D}{(1+\alpha_D)^2}
\right],
\]
showing how proportional and derivative feedback lower the measured amplitude-quadrature noise [2604.16202].

## 5. Applications in precision measurement and control

The most developed application of amplitude-quadrature squeezing is gravitational-wave interferometry. There, the quantum-noise spectrum decomposes into low-frequency quantum radiation-pressure noise, driven by the amplitude quadrature, and high-frequency shot noise, associated with the phase quadrature [2008.08094]. In an Advanced-LIGO-like interferometer with \(L_{\rm gw}=4\) km, \(m_{\rm gw}=40\) kg, \(\kappa_{\rm gw}/2\pi=100\) Hz, and \(P_{\rm gw}=10.6\) kW, injecting optomechanically generated frequency-dependent squeezing can outperform fixed-angle \(10\) dB squeezing, with up to about \(5.5\) dB sensitivity advantage above \(100\) Hz for \(\Delta=0\) and distinct low-frequency benefits for \(\Delta=-0.5\kappa\) [1602.03233]. A complementary strategy is the amplitude filter cavity: a \(16\) m critically coupled cavity on resonance attenuates low-frequency sidebands without rotating the squeezing ellipse, suppressing the amplitude anti-squeezing that otherwise worsens QRPN below about \(90\) Hz while preserving high-frequency phase squeezing [2008.08094]. In the demonstration, \(L=16.0611\pm 0.0002\) m, \(T=51.5\) ppm, round-trip loss \(=46\) ppm, storage time \(=2.1\pm 0.1\) ms, and observed frequency-independent squeezing with the cavity far off resonance was \(5\) dB, corresponding to about \(11\) dB generated squeezing after accounting for approximately \(21\%\) total path loss [2008.08094].

Dual-comb spectroscopy uses amplitude squeezing in a different way. In GHz repetition-rate dual-comb interferograms, large optical-path-delay regions are intensity-like, so amplitude-quadrature squeezing directly lowers the dominant shot noise [2408.16688]. A bright amplitude-squeezed comb of about \(15\) mW interfered with a weak coherent comb of about \(10\,\mu\)W enabled mode-resolved \(\mathrm{H_2S}\) spectroscopy over about \(20\) nm centered at \(1563\) nm, covering \(67\) rovibrational transitions with linewidths of about \(1\) GHz sampled by \(3\)–\(4\) RF modes each [2408.16688]. The reported SQZ/SNL prefactor ratio was about \(0.51\), corresponding to nearly \(2.9\) dB beyond the shot-noise limit in variance and a two-fold quantum speedup in concentration determination [2408.16688].

In semiconductor lasers, broadband amplitude squeezing is relevant to high-speed continuous-variable protocols because it is generated directly in the laser output without an external nonlinear stage [2309.09703]. The room-temperature \(3\)–\(12\) GHz bandwidth observed in QD lasers supports homodyne-based quantum information and sensing at multi-GHz rates [2309.09703]. This suggests a technological distinction between bright amplitude-squeezed laser sources and more conventional vacuum-squeezing architectures: the former are naturally compatible with direct detection and integrated photonic-electronic platforms.

Optomechanical and mechanical implementations translate amplitude squeezing into position-like quadratures. In a quadratically coupled membrane-in-the-middle system with periodically modulated drive, the mechanical position quadrature \(X_m=(b+b^\dagger)/\sqrt{2}\) is squeezed beyond the \(3\) dB limit through Bogoliubov-mode cooling, with robustness up to thermal occupancy \(10^4\) phonons [2210.00510]. In a micromechanical cantilever with feedback-enhanced parametric squeezing, single-quadrature feedback stabilized the anti-squeezed mode and enabled \(11.5\) dB squeezing for a sinusoidal test signal and \(11.3\) dB for thermomechanical noise, decisively beyond the conventional \(3\) dB parametric limit [1309.3121]. These cases show that the amplitude-quadrature concept extends naturally from optical intensity to mechanical displacement.

## 6. Limitations, controversies, and open technical issues

Loss is the most universal limitation. In direct form it obeys \(V_{\mathrm{obs}}=\eta V_{\mathrm{in}}+(1-\eta)\), so all platforms suffer the same basic degradation mechanism even when the microscopic origin of squeezing differs [2408.16688]. In the dual-comb experiment, overall optical and electronic efficiency to the analyzer was about \(78\%\), so \(3.8\) dB generated squeezing appeared as about \(2.6\) dB if electronics were not subtracted [2408.16688]. In the nanophotonic microresonator, the measured \(1.71\) dB squeezing and \(5.54\) dB anti-squeezing at \(20\) MHz sideband were consistent with only about \(37\%\) overall collection-and-detection efficiency, even though the ring outcoupling efficiency itself was about \(0.90\) [2502.17337]. In the fiber-coupled PPLN module, the dominant internal limitation was an effective \(25\%\) module loss attributed mainly to propagation and coupling [1906.09749].

A second persistent issue is anti-squeezing leakage. In optomechanical frequency-dependent squeezing, the strongest squeezing and anti-squeezing are both concentrated near \(\omega_{\rm eff}\), and even small homodyne-angle errors couple a large anti-squeezed spike into the readout [1602.03233]. The paper explicitly notes that locking errors up to \(6\%\) of a radian can generate a sharp noise spike around \(\omega_{\rm eff}\) [1602.03233]. The amplitude filter cavity solves a different version of the same problem by deliberately destroying low-frequency anti-squeezing through loss, which preserves sensitivity but cannot improve low-frequency QRPN beyond the unsqueezed level [2008.08094]. This is a recurring trade-off: aggressive suppression of amplitude anti-squeezing protects stability and low-frequency performance, but also removes potentially useful squeezing resources.

A third issue concerns hidden or frequency-complex squeezing. Standard monochromatic homodyne detection accesses only the real part of amplitude–phase cross-correlations, so some squeezing can remain invisible unless synodyne or resonator-assisted detection is used [2606.26266]. This matters especially in semiconductor lasers, optomechanics, and broadly multimode states, where the optimal quadrature rotates with frequency and may not correspond to a simple static amplitude axis [1602.03233][2606.26266]. A plausible implication is that reports framed purely in terms of “amplitude squeezing” may understate the exploitable nonclassical resource when the covariance matrix is complex and frequency resolved.

Finally, there is a conceptual misconception that amplitude squeezing always means direct intensity squeezing of a single optical mode. The literature here is broader. In gravitational-wave interferometry, “amplitude quadrature” refers to the quadrature that drives radiation-pressure back-action rather than merely photodetector current [1602.03233][2008.08094]. In mechanical and magnonic systems it denotes the position-like or in-phase quadrature of a bosonic mode [2210.00510][2304.07602]. In heralded probabilistic amplification, the transformation can increase the squeezing of whichever quadrature is already squeezed, while remaining phase-insensitive at the level of the Kraus operator \(T\propto g^{\hat n}\) [1205.4585]. The common structure is not the specific physical observable but the suppression of one canonical quadrature below its reference quantum noise.

## 7. Historical development and current outlook

Early discussions of quadrature squeezing emphasized fixed-axis optical squeezing, but later work established frequency dependence, hybrid matter couplings, and direct-source architectures as equally important. Atomic vapor experiments showed that hot \(^{87}\)Rb could generate low-sideband squeezed vacuum and manipulate its quadrature angle via EIT filtering without crystals or cavities [1204.3967]. Cavity optomechanics then sharpened the importance of amplitude-quadrature rotation in the acoustic band for SQL-beating interferometry [1602.03233]. Bichromatic homodyne detection made it possible to characterize squeezing across broadband, widely separated sidebands and directly observe a \(\pi/2\) rotation of the squeezing ellipse [1609.03196].

More recent work broadened the implementation space. Electrically driven QD lasers demonstrated room-temperature multi-GHz amplitude squeezing in a monolithic source [2309.09703]. Dual-comb spectroscopy showed that bright amplitude-squeezed combs can deliver nearly \(3\) dB beyond the SNL and a two-fold quantum speedup in a chemically relevant measurement [2408.16688]. Nanophotonic Si\(_3\)N\(_4\) resonators brought the field into foundry-compatible integrated photonics with \(7.8\) dB on-chip amplitude squeezing [2502.17337]. Semiconductor-laser theory then revealed complex and hidden quadrature squeezing, suggesting that the conventional distinction between amplitude and phase squeezing is incomplete once full frequency-resolved covariance matrices are considered [2606.26266].

Across these developments, three stable themes emerge. First, the physically useful quadrature is set by the measurement chain: direct detection favors amplitude squeezing, interferometric readout can require frequency-dependent rotation between amplitude and phase, and continuous-measurement protocols can define amplitude quadratures in rotating frames [2408.16688][1602.03233][2604.16202]. Second, compactness and integrability increasingly matter: fiber-coupled waveguide modules, semiconductor lasers, chip-integrated microresonators, and atomic cells all aim to replace bulk squeezed-light infrastructure with smaller platforms [1906.09749][2309.09703][2502.17337][1204.3967]. Third, the dominant obstacles remain loss, technical noise, and control of anti-squeezed correlations [1602.03233][2008.08094].

Amplitude-quadrature squeezing therefore occupies a dual role in contemporary quantum science. It is both a canonical textbook manifestation of reduced quadrature noise and a platform-dependent engineering resource whose exact value depends on how the amplitude axis is defined, rotated, preserved, filtered, or measured. The literature indicates that future progress will hinge less on the abstract existence of squeezing than on bandwidth, mode structure, controllable quadrature rotation, and loss management in the specific metrological architecture under consideration [1602.03233][2408.16688][2502.17337].

Source: https://www.emergentmind.com/topics/amplitude-quadrature-squeezing