Quantum-Enhanced Fiber Optic Gyroscope

• Quantum-enhanced FOGs are fiber Sagnac interferometers that use non-classical resources like NOON and squeezed states to reduce angular-velocity estimation variance.
• They achieve sub-shot-noise sensitivity and super-resolution by modifying phase responsivity and counting statistics within the interferometric measurement.
• Research spans entangled photon experiments, continuous-variable schemes, and atom–light hybrids, aiming to improve navigation and precision metrology under low-photon conditions.

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 (Fink et al., 2018, Grace et al., 2020).

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 $r$ (Fink et al., 2018).

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 $A$0 (Fink et al., 2018, Grace et al., 2020).

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 (Fink et al., 2018). For $A$1 photons, the state is

$A$2

and for $A$3 it becomes $A$4. After a relative phase $A$5, the fringe oscillation scales as $A$6. This produces $A$7-times denser fringes in $A$8 and an ideal sensitivity

$A$9

which is better by a factor $\Omega$0 than the SQL (Fink et al., 2018).

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$\Omega$1 crystal and coupling into a polarization-maintaining single-mode fiber. Measured rates were singles $\Omega$2/s and pairs $\Omega$3/s. A half-wave plate at $\Omega$4 converted $\Omega$5 into the polarization NOON state $\Omega$6, while a reference $\Omega$7 run used a transmitted $\Omega$8. A polarizing beam splitter injected the two polarizations into clockwise and counter-clockwise directions of a single-mode fiber coil of radius $\Omega$9 cm and length $\Delta t(\Omega)=\frac{4A\Omega}{c^2},$0 m (Fink et al., 2018).

For that coil, with $\Delta t(\Omega)=\frac{4A\Omega}{c^2},$1 nm, the scale factor was %%%%92$\Omega$92%%%%3. The measured fringe forms were

$\Delta t(\Omega)=\frac{4A\Omega}{c^2},$4

with fitted %%%%92$M$92%%%%6 for both runs and $\Delta t(\Omega)=\frac{4A\Omega}{c^2},$7 rad. The fringe-frequency ratio $\Delta t(\Omega)=\frac{4A\Omega}{c^2},$8 validated super-resolution. With total detected photons per bin $\Delta t(\Omega)=\frac{4A\Omega}{c^2},$9, the $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$0 SQL was $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$1 rad/s, the best one-photon run gave $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$2 rad/s, and the best two-photon run gave $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$3 rad/s, below the $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$4 SQL. The dominant noise was Poissonian count-rate fluctuation plus background $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$5 counts/bin, and no significant two-photon decoherence was observed over the coil length (Fink et al., 2018).

This experiment also clarifies a recurrent distinction. The doubled fringe frequency establishes super-resolution, but sub-SQL rotation sensitivity requires the stronger condition $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$6. In this case both were demonstrated, but they are not identical criteria (Fink et al., 2018).

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

$$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$7

and the corresponding enhancement factor over the classical design is

$$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$8

In the infinite-squeezing limit, $$\phi_S(\Omega)=\omega\Delta t(\Omega)\simeq \frac{4\pi A\Omega}{\lambda c}\equiv S_T\Omega, \qquad S_T=\frac{4\pi A}{\lambda c}.$$9, so under realistic loss the scaling returns to SQL behavior with a constant-factor quantum advantage. The same analysis reports diminishing returns beyond $A\approx Lr$0–$A\approx Lr$1 dB of squeezing (Grace et al., 2020).

Under a fixed total fiber-length constraint, the same work shows that splitting the available fiber into $A\approx Lr$2 identical Sagnac loops and feeding them with a single multi-mode-entangled squeezed-vacuum resource improves the rotation-estimation variance by a factor of $A\approx Lr$3 in the high-squeezing limit. The optimized entangled-loop variance is written as

$A\approx Lr$4

with $A\approx Lr$5 (Grace et al., 2020).

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 $A\approx Lr$6 beam-splitter network distributes the two modes, each pair traverses a separate FOG, and local homodyne receivers measure

$A\approx Lr$7

For the mode-entangled bTMSS scheme,

$A\approx Lr$8

while the separable case gives

$A\approx Lr$9

With $r$0 loss per channel, $r$1, and initial squeezing of $r$2 dB, the entangled network yields a phase-variance reduction of $r$3 dB below the shot-noise limit (Kannath et al., 2 Aug 2025).

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,

$r$4

With loss modeled by transmission $r$5,

$r$6

and sub-SNL operation requires

$r$7

For large $r$8, this approaches $r$9, namely less than $M$0 dB total loss. In the bright-seed limit, the direct intensity-difference measurement approaches the quantum Cramér–Rao bound (Xiao et al., 7 Jul 2026).

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

$M$1

which in the small-$M$2 regime simplifies to

$M$3

The associated small-$M$4 quantum Fisher information scales as

$M$5

and for fixed $M$6 it grows $M$7. 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 $M$8 loss $M$9 (Zhang et al., 2024).

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 $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$0 m$$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$1 and operating wavelength $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$2 nm. The detection limit was $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$3 zs over a $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$4 s averaging time and $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$5 zs in differential delay measurements at $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$6 s averaging, while the detection protocol saturated $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$7 of the Cramér–Rao bound in the differential readout (Sgobba et al., 2024). 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 $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$8 nm, $$\Delta\phi_{\rm SQL}=\frac{1}{\sqrt{M}}, \qquad \Delta\Omega_{\rm SQL}=\frac{1}{S_T\sqrt{M}}.$$9/shot, $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$0, $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$1 dB/km, loop diameter $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$2 m, and loop length $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$3 m, the optimized sensitivity is $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$4 rad/s/$$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$5 (Wu et al., 2020).

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 $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$6 uncorrelated photons impinge on the same detectors used for NOON coincidences, random temporal overlap within the detector jitter produces spurious coincidences. For an $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$7th-order N00N interferometer measured over time $$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$8,

$$\sigma^2_{\Omega,\,\rm C}=\frac{1}{T^2\eta N_v}=\frac{1}{T^2\eta\alpha^2},$$9

In the small-phase limit, the induced phase uncertainty is

$A$00

and sub-shot-noise operation requires $A$01 (Evans et al., 29 Sep 2025).

This noise is strongly bias dependent. Spurious-noise cusps occur at $A$02, while local minima appear when $A$03. The practical prescription is

$A$04

or equivalently $A$05 modulo $A$06. The reported effect is suppression of $A$07 by roughly an order of magnitude below the shot-noise floor (Evans et al., 29 Sep 2025).

The same analysis also quantifies the distance penalty of fiber loss. For two-photon states,

$A$08

and the maximum length for quantum advantage is approximated by

$A$09

For typical SPDC sources and $A$10 dB/km, $A$11 a few km for sub-shot-noise performance at Earth’s rotation rate (Evans et al., 29 Sep 2025).

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 (Grace et al., 2020, Xiao et al., 7 Jul 2026).

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 (Fink et al., 2018). 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 (Kannath et al., 2 Aug 2025).

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 (Fink et al., 2018). Continuous-variable squeezing and entanglement offer brighter probes and more scalable detection, but realistic loss usually converts asymptotic scaling advantages into constant-factor improvements (Grace et al., 2020). Bright two-mode squeezing and coherent boosting are aimed precisely at retaining substantial advantage in lossy conditions (Kannath et al., 2 Aug 2025, Xiao et al., 7 Jul 2026). 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 (Zhang et al., 2024, Sgobba et al., 2024).

Several concrete technological directions recur across the field: brighter entangled sources such as waveguide SPDC or quantum dots, superconducting photon counters with efficiency $A$12 and low dark noise, integrated-photonics Sagnac loops for mechanical and thermal stability, and operation in the telecommunications band $A$13–$A$14 $A$15 for low fiber loss (Fink et al., 2018). 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.