Relational Environment Spectroscopy from Qutrit Coherence Geometry

A reduced qutrit does not only lose coherence under environmental coupling; it loses coherence with a geometry. This preprint shows that the pairwise coherence structure of a qutrit contains a directly accessible fingerprint of environmental distinguishability. By normalizing the three pair coherences with respect to the corresponding populations, one obtains a reduced-state map that identifies which pairs of qutrit alternatives remain mutually indistinguishable, which pairs are resolved by the environment, and which sectors may be protected or rephased. The method is deliberately economical. It does not attempt full bath reconstruction, process-tensor tomography, or spectral noise reconstruction. Instead, it uses only the reduced qutrit populations and pairwise coherences, or equivalently calibrated pairwise visibilities in an interferometric implementation. The resulting three-component distinguishability map gives the environmental structure as seen by the qutrit. Under additional model assumptions it can be interpreted as an environmental record-overlap map, a scalar coupling-distance diagnostic, a vector-noise metric, or a pair-selective memory fingerprint. The reconstruction is relational rather than microscopic. Different reservoirs may be indistinguishable to the qutrit if they generate the same reduced coherence geometry. The paper therefore identifies the equivalence class of environmental structures visible to the three-level probe. Explicit examples illustrate scalar Gaussian dephasing, protected pairs, vector or correlated-noise geometry, pair-selective recoherence, and safe analysis windows when populations or coherences approach a noise floor.