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.
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.
This preprint introduces a dynamical qutrit coherence-cycle witness based on calibrated pairwise visibility measurements in a three-path interferometer. The central idea is that pairwise visibility data contain a geometry of normalized qutrit coherences that is not captured by scalar coherence measures alone. For nonzero path populations, the population-calibrated two-path visibility equals the normalized off-diagonal coherence of the reduced path qutrit. The squared normalized coherences define the cycle expression Scyc = kappa_12^2 + kappa_23^2 - kappa_13^2. Classical jointly diagonalizable overlap geometries obey the boundary Scyc <= 1. A statistically certified value Scyc > 1 therefore indicates a nonclassical cyclic arrangement of pair coherences, rather than merely a large amount of coherence. The paper proves the physical qutrit range Scyc <= 5/4, gives explicit positive semidefinite qutrit examples with equal scalar coherence but different cycle geometry, constructs a completely positive random-unitary dephasing model with time-dependent geometry windows, and formulates a finite-data certification protocol including calibration and covariance propagation. The static overlap-cycle inequality is imported from prior overlap-cycle work; the new contribution is its calibrated realization as a path-qutrit coherence-geometry witness. The proposed witness is intended as a measurement-efficient diagnostic of normalized coherence geometry in multipath interferometry and open qutrit dynamics. It is not a full state-tomography method and does not by itself constitute a complete contextuality experiment; stronger interpretations require the additional operational assumptions stated in the manuscript.
We identify the qutrit as the minimal Hilbert-space dimension in which coherence amountand coherence sharing become operationally distinguishable. The starting point is theexact purity decomposition into population predictability, Hilbert–Schmidt coherence, andmixedness. Although this closure is a state-space identity, in dimension three it selects aEuclidean coherence coordinate that can be compared nontrivially with normalized ℓ1coherence. Their mismatch defines a positive deficit Δℓ1 that vanishes if and only if thethree pairwise coherence moduli are equal. The deficit therefore diagnosescoherence-sharing anisotropy rather than total coherence magnitude alone. We show thatΔℓ1 separates two physically distinct mechanisms of coherence reduction: populationanisotropy in symmetric channels and branch asymmetry in balanced qutrits. In a purifiedqutrit–meter model the same Euclidean language acquires a dynamical interpretationbecause reduced mixedness equals normalized linear-entropy entanglement across thesystem–meter cut. We clarify the resource-theoretic status of the diagnostic by showingthat it is not a coherence monotone, but a witness of unequal sharing among pairwisechannels. Finally, we give a reduced-state reconstruction protocol based on populationsand three embedded SU(2) Ramsey blocks, supported by finite-sample simulations. Thesame quantity has a direct three-path interferometric implementation in terms of pairwisefringe visibilities and calibrated path intensities, where it measures anisotropicmutual-coherence sharing rather than a universal violation of classical coherence theory.
This work formulates dynamical-decoupling (DD) spectroscopy as a reduced observation problem. Rather than treating measured coherence responses as direct probes of the full environmental noise spectrum, the paper introduces a protocol-dependent map from parametrized spectral families to a small set of observables and analyzes its local Jacobian structure. The main result is a geometric framework in which spectral directions are classified into observable, weakly observable, and compressed sectors according to the singular-value structure and effective rank of the reduced map. Within this framework, plateau behavior and fixed protocol ratios arise when the reduced image becomes effectively low-dimensional, while abrupt transitions are interpreted as switching between response sectors with different local observability structure. A running power-law example is used to illustrate how amplitude and slope deformations are transmitted differently into protocol observables, and how protocol ratios can become locally insensitive without implying full spectral universality. The analysis emphasizes that DD protocols access environmental structure only through compressed, protocol-shaped images of the underlying spectrum. This provides a unifying interpretation of several familiar DD phenomena, including plateau regions, fixed-ratio structures, and sharp protocol-level transitions, in terms of reduced observation geometry rather than direct spectral reconstruction. v2 :This work formulates dynamical-decoupling spectroscopy as a reduced observation map from parameterized noise spectra to protocol-level observables. Using the Jacobian of this map, we classify spectral directions into observable, weakly observable, and compressed sectors via an effective-rank criterion. Plateau behavior and fixed protocol ratios are shown to arise from geometric compression of the reduced image, combined with a proportional-locking condition, rather than from full spectral universality. Abrupt transitions are interpreted as switching between response sectors with different local observability structures. The framework provides a unified geometric interpretation of sensitivity, compression, and invariance in DD-based noise spectroscopy.
This repository accompanies the preprint “Mapping the Limits of Architecture-Sensitive Noise Fingerprints in Quantum States.” The work investigates when and why simple classical measurement statistics obtained from noisy quantum systems retain information about the underlying quantum state architecture, and when such information collapses entirely. Building on earlier results demonstrating the existence of architecture-dependent classical fingerprints for stabilizer states under local noise, this study systematically maps the boundaries and failure modes of that phenomenon. Using exact probability distributions for small-to-moderate system sizes, we introduce controlled departures from stabilizer structure and track the degradation of classical features under dephasing and depolarizing noise. The analysis reveals sharply conditional survival of architecture sensitivity, a consistent feature-dependent collapse ordering, and a strong dependence on measurement basis and perturbation geometry. In particular, regimes of genuine diagnostic blindness are identified, where classical statistics become architecture-indistinguishable even though the underlying quantum states remain highly structured. The archive includes the full manuscript (PDF and LaTeX source), all figures appearing in the paper, the scripts required to reproduce the numerical experiments and figures, and the corresponding data outputs. All results are based on exact numerical evaluation (no sampling, optimisation, tomography, or machine learning). The work is intended as a lightweight, diagnostic limits study, providing practical guidance on when simple classical measurements are informative and when their use is fundamentally unreliable. Together with the companion papers in this series, the repository contributes to a coherent empirical and theoretical programme on the classical observability of quantum structure under noise.Version 1.1 notes.This revision clarifies the collapse criterion used to define architecture indistinguishability, explicitly specifies numerical precision and robustness checks, and adds a qualitative reliability chart summarising when different classical features remain informative. The presentation of noise-model dependence, system-size stability, and perturbation geometry has been sharpened, and the relationship to companion papers in the series has been made explicit. No new phenomena are introduced; the update improves transparency, interpretability, and practical usability of the results.
When does operational distinguishability contain sufficient information to identify physical structure? We address this question through a resource-relative framework of Operational Informational Distinguishability (OID), designed to investigate the mathematical consistency of identifiability across quantum states, information geometry, and physical processes. An operational observer is characterized by (\mathcal{D}=(\mathcal{A},\mathcal{M},\mathcal{R},\delta)), whose labelled outcome distributions define an operational signature and induce equivalence classes of physically indistinguishable realizations. We establish an exact reconstruction criterion: a proposed geometric assignment factors uniquely through the operational signature if and only if it is constant on these equivalence classes. This provides a necessary-and-sufficient condition for operational reconstruction, while separating identifiability from the additional requirements of local non-degeneracy and stability. For faithful finite-dimensional quantum-state manifolds, we establish the measurement–information-geometric hierarchy[g^{(\mathcal{M})}\preceq g^{\mathrm{SLD}}\preceq g^{\mathrm{BKM}}relating measurement-restricted Fisher information, the symmetric logarithmic derivative metric, and the Bogoliubov–Kubo–Mori metric. We clarify the directional attainability of the SLD bound and its distinction from simultaneous multiparameter attainability. As an explicit algebraic result, we characterize the operator span generated by diagonal phase modulation of cyclic-shift eigenstate projectors in the one-excitation sector: it is precisely the constant-diagonal Hermitian subspace, of dimension (N^{2}-N+1), leaving (N-1) independent population directions unresolved. Adjoining site-basis projectors restores informational completeness. This idealized construction is connected to experimentally realized entangled measurements of (W) states. We further extend operational distinguishability to quantum processes through tester-restricted signatures and divergences, explicitly separating signalling from intervention-defined causal influence. Finally, we introduce accumulated information-geometric path length as a candidate operational clock parameter, without identifying it with physical time. By relating these constructions to holographic information-distance bounds, bulk entanglement, conditional mutual information and recovery, and recent approaches to emergent geometry and informational time, we formulate a central testable question: can a common resource-relative distinguishability structure remain identifiable, stable, and compositionally consistent across states, processes, geometry, temporal ordering, and causality? The framework makes both constructive reconstruction and mathematically explicit obstructions possible, providing a falsifiable methodological program rather than presupposing the emergence or unification of physical structure.
The irreversible emergence of classical behavior from a reduced quantum description via a canonical intrinsic decomposition of the density operator is analyzed. In the intrinsic reference basis (IRB), defined for a fixed physical conjugation K (determined by measurement convention, system symmetry, or secular approximation) by diagonalizing the real symmetric part of the state, the density operator separates into a diagonal population sector and a real antisymmetric coherence sector. For the class of Markovian open-system dynamics whose Lindblad operators are diagonal in the IRB, we prove that the quadratic coherence functional is a Lyapunov functional under pure-dephasing or interaction-picture evolution, with each intrinsic coherence component decaying exponentially at a computable rate. This yields a canonical state-dependent operational classicality criterion via the normalized cohesion index, an explicit logarithmic classicalization time controlled by the slowest dephasing rate, and a demonstration that the IRB projectors emerge as dynamically stable pointer sectors under IRB-selective evolution. Suppression of intrinsic coherences is exactly equivalent to suppression of fringe visibility in the corresponding interferometric sector; for a balanced two-path setup the cohesion index coincides with the fringe visibility, making the classicality criterion directly testable with standard interferometric equipment. The approach complements environment-induced einselection: it is applicable whenever a coarse-grained reduced description is available, independently of whether the microscopic system-environment coupling is known.