---
title: Quantum-Enhanced Fiber Optic Gyroscope
url: https://www.emergentmind.com/topics/quantum-enhanced-fiber-optic-gyroscope-fog
type: topic
---

# Quantum-Enhanced Fiber Optic Gyroscope

Quantum-enhanced fiber optic gyroscopes are fiber Sagnac interferometers whose rotation readout is improved by non-classical optical states or correlated atom–light resources so as to surpass the standard quantum limit, reduce angular-velocity estimate variance under fixed resources, or preserve sensitivity in low-photon regimes. In the classical fiber optic gyroscope, counter-propagating fields acquire a Sagnac phase proportional to angular velocity; in quantum-enhanced variants, path-entangled NOON states, squeezed and two-mode-squeezed resources, non-Gaussian probes, heralded single-photon states, and distributed entanglement modify either the phase responsivity, the counting statistics, or both [1810.02213, 2003.12545].

## 1. Sagnac transduction and the standard quantum limit

A fiber optic gyroscope relies on the Sagnac effect. For an interferometer with total optical path length \(L\) and effective enclosed area \(A\), rotation at angular velocity \(\Omega\) produces a relative delay
\[
\Delta t(\Omega)=\frac{4A\Omega}{c^2},
\]
and hence a phase shift
\[
\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega,
\qquad
S_T=\frac{4\pi A}{\lambda c}.
\]
In a fiber coil, the effective area is amplified by winding many turns, with \(A\approx Lr\) for coil radius \(r\) [1810.02213].

For classical optical inputs, phase estimation is bounded by shot noise. If \(M\) photons are detected, the classical phase uncertainty is
\[
\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}},
\qquad
\Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.
\]
The same scaling appears in homodyne-based analyses of a laser-driven FOG. In that formulation, the estimator variance is
\[
\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},
\]
which is the SQL scaling \(\propto 1/N_v\) [1810.02213, 2003.12545].

The central objective of a quantum-enhanced FOG is therefore not to alter the Sagnac transduction itself, but to change the metrological scaling or constant prefactor attached to the readout noise. The literature represented here divides broadly into discrete-variable entanglement schemes, continuous-variable squeezing and entanglement schemes, non-Gaussian probe proposals, low-photon single-photon gyroscopes, and hybrid atom–light architectures.

## 2. Entangled-photon fiber gyroscopes based on NOON states

The first direct experimental demonstration of sub-SQL rotation measurement in a Sagnac interferometer used two-photon path-entangled NOON states [1810.02213]. For \(N\) photons, the state is
\[
\bigl|\Psi_{\rm NOON}^{(N)}\bigr\rangle
=\frac{1}{\sqrt2}\Bigl(|N_{\circlearrowright},0_{\circlearrowleft}\rangle
+
|0_{\circlearrowright},N_{\circlearrowleft}\rangle\Bigr),
\]
and for \(N=2\) it becomes \(\tfrac1{\sqrt2}(|2,0\rangle+|0,2\rangle)\). After a relative phase \(\phi\), the fringe oscillation scales as \(\cos^2(N\phi/2)\). This produces \(N\)-times denser fringes in \(\phi\) and an ideal sensitivity
\[
\Delta\phi_{\rm NOON}=\frac{1}{\sqrt{NM}},
\qquad
\Delta\Omega_{\rm NOON}=\frac{1}{S_T\sqrt{NM}},
\]
which is better by a factor \(\sqrt{N}\) than the SQL [1810.02213].

The experimental realization used a continuous-wave 405 nm diode laser pumping a periodically poled KTP crystal. Type-II SPDC generated H- and V-polarized photons at 810 nm, followed by temporal compensation with an extra Nd:YVO\(_4\) crystal and coupling into a polarization-maintaining single-mode fiber. Measured rates were singles \(N_S\approx950{,}000\)/s and pairs \(\approx191{,}000\)/s. A half-wave plate at \(22.5^\circ\) converted \(|1_H,1_V\rangle\) into the polarization NOON state \(\tfrac1{\sqrt2}(|2_H,0_V\rangle-|0_H,2_V\rangle)\), while a reference \(N=1\) run used a transmitted \(|1_H,0_V\rangle\). A polarizing beam splitter injected the two polarizations into clockwise and counter-clockwise directions of a single-mode fiber coil of radius \(\sim 7.8\) cm and length \(270.5\) m [1810.02213].

For that coil, with \(\lambda=810\) nm, the scale factor was \(S_T\approx1.09\)\(({\rm rad\,s}^{-1})^{-1}\). The measured fringe forms were
\[
R_1\propto \cos^2\!\Bigl(\tfrac12(S\Omega+\phi_0)\Bigr),
\qquad
R_2\propto \cos^2\!\Bigl(S\Omega+\phi_0\Bigr),
\]
with fitted \(S=1.09\)\(({\rm rad\,s}^{-1})^{-1}\) for both runs and \(\phi_0\approx1.67\) rad. The fringe-frequency ratio \(\omega_2/\omega_1=1.995(4)\approx2\) validated super-resolution. With total detected photons per bin \(M\approx1955\), the \(N=1\) SQL was \(\Delta\Omega_{\rm SQL}\approx0.0207\) rad/s, the best one-photon run gave \(\Delta\Omega_{\min}^{(1)}=0.0250(2)\) rad/s, and the best two-photon run gave \(\Delta\Omega_{\min}^{(2)}=0.0189(4)\) rad/s, below the \(N=1\) SQL. The dominant noise was Poissonian count-rate fluctuation plus background \(B\approx50\) counts/bin, and no significant two-photon decoherence was observed over the coil length [1810.02213].

This experiment also clarifies a recurrent distinction. The doubled fringe frequency establishes super-resolution, but sub-SQL rotation sensitivity requires the stronger condition \(\Delta\Omega_{\min}^{(2)}<\Delta\Omega_{\rm SQL}\). In this case both were demonstrated, but they are not identical criteria [1810.02213].

## 3. Continuous-variable squeezing, bright entanglement, and distributed architectures

A separate line of work analyzes squeezed-vacuum and continuous-variable entanglement as the quantum resource for the FOG. In a single-interferometer design with one coherent input and one squeezed-vacuum input, homodyne detection gives
\[
\sigma^2_{\Omega,\,\rm S}
=
\frac{\eta e^{-2r}+1-\eta}{T^2\eta N_v},
\]
and the corresponding enhancement factor over the classical design is
\[
G(r,\eta)=\frac{1}{\eta e^{-2r}+(1-\eta)}.
\]
In the infinite-squeezing limit, \(G\to 1/(1-\eta)\), so under realistic loss the scaling returns to SQL behavior with a constant-factor quantum advantage. The same analysis reports diminishing returns beyond \(10\)–\(15\) dB of squeezing [2003.12545].

Under a fixed total fiber-length constraint, the same work shows that splitting the available fiber into \(M\) identical Sagnac loops and feeding them with a single multi-mode-entangled squeezed-vacuum resource improves the rotation-estimation variance by a factor of \(e\approx2.718\) in the high-squeezing limit. The optimized entangled-loop variance is written as
\[
\sigma^2_{\Omega,\,\rm E}
=
\frac{1}{T^2\eta_M M n_v}\bigl(\eta_M e^{-2r}+1-\eta_M\bigr),
\]
with \(\eta_M=10^{-b(L/M)/10}\) [2003.12545].

A more recent distributed-network proposal replaces discrete single-loop enhancement by a global estimation strategy over multiple gyroscopes using bright two-mode squeezed states. A seeded OPA or FWM source generates a bTMSS, a symmetric \(M\times M\) beam-splitter network distributes the two modes, each pair traverses a separate FOG, and local homodyne receivers measure
\[
Y_j=\frac{1}{\sqrt2}\bigl(\hat Y_{a'_j}+\hat Y_{b'_j}\bigr),
\qquad
Y_+=\sum_{j=1}^M Y_j.
\]
For the mode-entangled bTMSS scheme,
\[
\Delta\phi^2_{\rm ent}
=
\frac{e^{-2r}+\tfrac1\eta-1}{2\alpha^2 e^{2r}},
\]
while the separable case gives
\[
\Delta\phi^2_{\rm sep}
=
\frac{e^{-2r}+\tfrac1\eta-1}{2M\beta^2 e^{2r}}.
\]
With \(5\%\) loss per channel, \(\eta=0.95\), and initial squeezing of \(\sim 9.8\) dB, the entangled network yields a phase-variance reduction of \(\sim 9.3\) dB below the shot-noise limit [2508.01447].

Another theoretical route uses coherently boosted two-mode squeezed beams injected into a fiber-optic Sagnac loop and read out by simple intensity-difference measurement. In the balanced optimal case,
\[
\Delta\phi \approx \frac{e^{-2r}}{\sqrt{N_{\rm tot}}},
\qquad
R\equiv \frac{\Delta\phi^2}{\Delta\phi^2_{\rm SNL}}=e^{-2r}.
\]
With loss modeled by transmission \(T\),
\[
R_{\rm loss}=e^{-2r}+\frac{1-T}{T},
\]
and sub-SNL operation requires
\[
T>\frac{1}{2-e^{-2r}}.
\]
For large \(r\), this approaches \(T>1/2\), namely less than \(3\) dB total loss. In the bright-seed limit, the direct intensity-difference measurement approaches the quantum Cramér–Rao bound [2607.05732].

## 4. Non-Gaussian probes, single-photon operation, and hybrid gyroscopes

Non-Gaussian-state proposals seek sensitivity gains beyond Gaussian squeezing at fixed photon budget. One such QFOG scheme uses a product probe consisting of a photon-added coherent state in one input mode and a coherent state in the other. Homodyne detection of the output quadrature gives
\[
\Delta\Omega^2_{\rm NG}
=
\frac{1}{
T^2\left\{\left[4\Delta X_{1,a}^2-1\right]\sin^2\phi
+
(1/\gamma)\left[\langle X_{1,a}\rangle\cos\phi+y\sin\phi\right]^2
\right\}},
\]
which in the small-\(\phi\) regime simplifies to
\[
\Delta\Omega^2_{\rm NG}\approx [T^2\gamma\langle X_{1,a}\rangle^2]^{-1}.
\]
The associated small-\(\phi\) quantum Fisher information scales as
\[
F_Q^{\rm NG}(m)=4\gamma\alpha^2\left[\frac{L_m^1(-\alpha^2)}{L_m(-\alpha^2)}\right]^2,
\]
and for fixed \(\alpha\) it grows \(\sim (m+1)^2\). Under fixed total input photon number, the reported sensitivity can be three orders of magnitude higher than coherent-state and squeezed-state probes for certain values of the measured parameter, and the advantage persists even with \(50\%\) loss \((\gamma=0.5)\) [2406.02217].

At the opposite end of the resource spectrum, an all-fiber telecom-range optical gyroscope based on heralded single photons and traced-out thermal-light statistics demonstrated zeptosecond-scale delay sensing. The device used a 2 km spool of single-mode, polarization-maintaining fiber in a quadrupole configuration, with effective enclosed area \(\mathcal A=125\) m\(^2\) and operating wavelength \(1550\) nm. The detection limit was \(249\) zs over a \(72\) s averaging time and \(26\) zs in differential delay measurements at \(t=10^4\) s averaging, while the detection protocol saturated \(>99.5\%\) of the Cramér–Rao bound in the differential readout [2402.15385]. Although this scheme does not use multi-photon entanglement, it is part of the same broader movement toward quantum-limited, low-photon fiber gyroscopy.

A distinct adjacent architecture is the atom–light hybrid quantum gyroscope. Here, an optical Sagnac loop is combined with an atomic ensemble acting as a quantum beam splitter/recombiner via Raman amplification. The rotation sensitivity can beat the SQL in ideal conditions and remains better than that of a FOG under practical attenuation. For \(\lambda=795\) nm, \(N_{\rm in}\approx10^8\)/shot, \(G_1=6\), \(\alpha_T=3\) dB/km, loop diameter \(D=0.2\) m, and loop length \(L=520\) m, the optimized sensitivity is \(\Delta\Omega_{\rm ALHQG}\simeq2.9\times10^{-8}\) rad/s/\(\sqrt{\rm Hz}\) [2009.06166].

## 5. Loss, saturation noise, and optimal biasing

The dominant practical limitation in long-fiber, higher-order NOON-state FOGs has been analyzed as uncorrelated photon saturation. If \(M_1\) uncorrelated photons impinge on the same detectors used for NOON coincidences, random temporal overlap within the detector jitter produces spurious coincidences. For an \(N\)th-order N00N interferometer measured over time \(t_{\rm meas}\),
\[
\Delta P_{\rm cc}
=
\left(\frac{M_1}{N}\right)^N
(\tau_{\rm jitter} t_{\rm meas})^{N-1}.
\]
In the small-phase limit, the induced phase uncertainty is
\[
\Delta\phi_P^0
=
\frac{2}{N}\sqrt{\frac{\Delta P_{\rm cc}}{M_{\rm N00N}}},
\]
and sub-shot-noise operation requires \(\Delta\phi_P < \Delta\phi_{\rm QM}=1/\sqrt{NM}\) [2509.25159].

This noise is strongly bias dependent. Spurious-noise cusps occur at \(\Phi=n\pi/2\), while local minima appear when \(N\Phi=(2n+1)\pi/2\). The practical prescription is
\[
\phi_0^{\rm opt}=\frac{(2n+1)\pi}{2N}-\phi_{\rm SL},
\]
or equivalently \(\phi_0\approx \pi/(2N)-\phi_{\rm SL}\) modulo \(\pi/N\). The reported effect is suppression of \(\Delta\phi_P\) by roughly an order of magnitude below the shot-noise floor [2509.25159].

The same analysis also quantifies the distance penalty of fiber loss. For two-photon states,
\[
M_{\rm N00N}(L)=M_{\rm N00N}(0)\,10^{-\alpha L/5},
\]
and the maximum length for quantum advantage is approximated by
\[
L_{\max}\approx \frac{5}{\alpha}\log_{10}\!\Bigl[\frac{M_{\rm N00N}(0)}{M_{\rm th}}\Bigr].
\]
For typical SPDC sources and \(\alpha\approx0.2\) dB/km, \(L_{\max}\sim\) a few km for sub-shot-noise performance at Earth’s rotation rate [2509.25159].

These results sharpen a broader methodological point. Lossless analyses can exhibit Heisenberg scaling or near-Heisenberg behavior, as in bright two-mode squeezing or ideal NOON-state arguments, but realistic fiber loss can reduce the improvement to a constant factor or impose explicit transmission thresholds for sub-SNL performance [2003.12545, 2607.05732].

## 6. Applications, performance regimes, and outlook

The application space is the same as for classical FOGs—sensing and navigation in spacecraft, aircraft, and autonomous vehicles—but with the added possibility of quantum enhancement without increasing optical power [1810.02213]. Distributed quantum sensing generalizes this to networks of gyroscopes estimating an average angular rotation across spatially separated nodes, with stated relevance to quantum-enhanced inertial navigation, precision metrology, and emerging quantum networks [2508.01447].

The current literature indicates several distinct operating regimes. Entangled-photon NOON-state experiments have already demonstrated sub-SQL rotation sensitivity per detected photon in a compact fiber Sagnac loop [1810.02213]. Continuous-variable squeezing and entanglement offer brighter probes and more scalable detection, but realistic loss usually converts asymptotic scaling advantages into constant-factor improvements [2003.12545]. Bright two-mode squeezing and coherent boosting are aimed precisely at retaining substantial advantage in lossy conditions [2508.01447, 2607.05732]. Non-Gaussian-state probes seek stronger gains under fixed photon number, whereas single-photon gyroscopes emphasize resource efficiency and ultimate delay sensitivity in the low-photon regime [2406.02217, 2402.15385].

Several concrete technological directions recur across the field: brighter entangled sources such as waveguide SPDC or quantum dots, superconducting photon counters with efficiency \(>90\%\) and low dark noise, integrated-photonics Sagnac loops for mechanical and thermal stability, and operation in the telecommunications band \(1.3\)–\(1.5\) \(\mu{\rm m}\) for low fiber loss [1810.02213]. This suggests that the near-term development path is not a single dominant architecture, but a convergence between low-loss telecom fiber platforms, more robust quantum resources, and estimation protocols that remain close to the quantum Cramér–Rao bound under realistic loss and drift.

In that sense, the quantum-enhanced FOG is less a single device class than a family of interferometric rotation sensors unified by the Sagnac phase and differentiated by how quantum resources are used: to sharpen fringe slope, suppress estimator variance, distribute information across multiple loops, or preserve high sensitivity at low optical power.

Source: https://www.emergentmind.com/topics/quantum-enhanced-fiber-optic-gyroscope-fog