Quantum Fisher Information as a Probe of Sterile Neutrino New Physics: Geometric Advantage of KM3NeT over IceCube

The detection of a 220 PeV neutrino event KM3-230213A at KM3NeT [1] and its non-observation at IceCube presents a tension of 2σ–3.5σ [2], recently resolved in [3] via sterile to active neutrino oscillations along the ∼147 km traversal path to KM3NeT, driven either by a matter induced MSW resonance parameterized by ϵss, or by off-diagonal nonstandard interactions (NSI) parameterized by ϵµs. We apply the Quantum Fisher Information (QFI) framework to quantify how much information the propagating neutrino state encodes about each new physics parameter {ϵss, ϵµs, ms} as a function of detector baseline, and what precision any measurement strategy can fundamentally achieve via the quantum Cram´er-Rao bound (QCRB). For the MSW scenario, FQ(ϵss) at KM3NeT’s 147 km baseline exceeds that at IceCube’s 14 km baseline by ∼3 orders of magnitude, with the QCRB establishing ∆ϵ KM3NeT ss ≳ O(12.7) versus ∆ϵ IceCube ss ≳ O(419) per event, requiring IceCube O(33) more detections to match KM3NeT’s single event precision. For the NSI scenario, the QFI ratio between detectors is independent of ϵµs, with ∆ϵKM3NeT µs ≳ O(5.1) versus ∆ϵ IceCube µs ≳ O(105). We identify an optimal baseline Lopt ≈ 150–200 km minimizing the QCRB, near which KM3NeT is situated, and show that the standard flavor projection measurement saturates the QCRB, leaving no room for improvement through exotic measurement strategies. These results establish that the KM3NeT-IceCube tension reflects a fundamental asymmetry in quantum information content of the neutrino state, and that O(5–10) future KM3NeT events would enable the first quantum limited measurement of sterile neutrino new physics couplings.