Quantum-sensor models: what Kshana models, and what it does not

Kshana is a PNT-resilience (PNT: positioning, navigation and timing) simulator with quantum-sensor performance models. It is not a first-principles quantum-physics simulator. This page states exactly what that means so the "quantum" framing cannot be mistaken for more than it is.

What IS modelled#

Each quantum (and classical) sensor is an error model driven by published noise-budget parameters:

• Clocks — white-frequency and random-walk-frequency PSDs (power spectral densities), a flicker (1/f) Allan floor, and linear drift, sourced from datasheets and papers: the CSAC (chip-scale atomic clock) Microchip SA.45s; the strontium optical-lattice clock of Origlia et al. (arXiv:1503.08457), a space-oriented goal; and the six ClockClass defaults (CSAC; USO, ultra-stable oscillator; DSAC, Deep Space Atomic Clock; TCXO, temperature-compensated crystal oscillator; OCXO, oven-controlled crystal oscillator; RAFS, rubidium atomic frequency standard), each citing one source. The Allan deviation these produce is validated against the standard noise-type slopes (see VALIDATION.md). One optical-clock curve is real: the measured ⁸⁸Sr tweezer-clock Allan deviation of Norcia et al. (Science 2019) is reproduced by the noise fit, a VALIDATED row in VERIFICATION-MATRIX.md; the holdover figures built on the optical class stay MODELLED.
• Inertial sensors — in the inertial and hybrid packs, a single-axis (1-DOF, one degree of freedom) accelerometer/gyro error budget: velocity random walk, angular random walk, acceleration random walk, and an Allan bias-instability floor. The gnss-ins and hybrid-ukf kinds instead run the three-axis strapdown mechanisation in src/inertial/ (quaternion attitude, north-east-down navigation equations, a deterministic IMU error model).
• The quantum scenario kinds — quantum-trade, quantum-time-transfer, quantum-anomaly-detect, quantum-gnss-free-nav and hybrid-ukf — are built from these error models and are MODELLED; quantum-time-transfer, quantum-anomaly-detect and quantum-gnss-free-nav also report a representativeness record with the gaps to flight.
• The engine is neutral: "quantum" and "classical" are the same code path with different coefficients. The contrast in the figures of merit comes entirely from the input noise parameters, each traceable to a cited source.

What is NOT modelled#

For the clock and time-transfer sensors, none of the underlying quantum physics is simulated — only the net Allan contribution, supplied as a coefficient. For the cold-atom accelerometer a first-principles layer now exists (see below); the remaining systematics are still coefficient-level or unmodelled:

• the atom-interferometer Mach–Zehnder phase (Φ = k_eff·a·T²), quantum projection / shot noise (σ_Φ = 1/(C·√N)), interferometer contrast decay, cycle time, and the vibration-coupling transfer function (|H(ω)| = (4/ω²)sin²(ωT/2), white-PSD variance σ_Φ² = k_eff²·S_a·T³/3) are now modelled from first principles for the CAI (cold-atom interferometer) accelerometer (src/inertial/quantum_imu.rs), deriving the white-acceleration PSD q_va the classical model consumes, together with the fringe-ambiguity dynamic range (a_max = π/(k_eff·T²)) — see QUANTUM.md;
• the Coriolis systematic (coriolis_phase / coriolis_accel_bias, the 2·v⊥·Ω cross-coupling) and the AC-Stark (AC: alternating-current) / light-shift systematic (ac_stark_phase, which cancels under a symmetric two-photon detuning) are now modelled and unit-tested in src/inertial/quantum_imu.rs;
• still not modelled: laser-phase noise, wavefront aberration, unwrapping a fringe reading beyond ±a_max, and clock-side first-principles physics;
• the quantum-versus-classical inertial pack is single-axis; the three-axis strapdown path runs only in gnss-ins and hybrid-ukf (see the IMU, inertial measurement unit, note in the README and VALIDATION.md).

Completing the quantum-physics layer (laser-phase noise, wavefront aberration and clock-side first-principles physics) is the remaining P2 work in ROADMAP.md.

Ground-lab vs. flight-qualified figures#

Parameter tables mix maturity levels; treat them accordingly:

Optical-clock figures in Kshana are space goals on ground hardware. No flown optical clock exists; the README and result provenance say so explicitly.

Benchmark: ACES/PHARAO on the ISS (operational since April 2025)#

The ESA (European Space Agency) ACES/PHARAO payload (ACES: Atomic Clock Ensemble in Space; PHARAO: Projet d'Horloge Atomique par Refroidissement d'Atomes en Orbite) — a laser-cooled caesium clock plus an active hydrogen maser, operating on the ISS (International Space Station) since April 2025 — is the current operational on-orbit clock-stability benchmark (target fractional stability of order 1e-16 after a few days of integration). Kshana's optical-clock model represents a more aggressive ground-lab goal than ACES's flown caesium/maser performance; when comparing Kshana's optical numbers to "what has actually flown", ACES/PHARAO is the honest reference point, and it is a microwave/maser system, not an optical-lattice clock.

The exact ACES in-orbit performance figures should be cited from ESA's published results as they are released; the point here is the maturity gap, not a specific number — Kshana's optical figures are goals, not flown performance.

See also#

• VALIDATION.md — per-parameter validated / not modeled labels.
• GLOSSARY.md — figure-of-merit (FoM) definitions and every abbreviation.
• INTEGRITY.md — what the Integrity and Security FoMs are and are not.
• QUANTUM.md — the first-principles cold-atom accelerometer.