claimFor any occupied spectral partition of an SLD-regular one-parameter quantum model, the Fisher-information loss equals the state-weighted within-bin SLD score variance and is at most one quarter of the state-weighted squared bin diameters; consequently any occupied bins of diameter at most delta lose at most delta squared divided by four.
RO-2026-0001:C1
claimThe optimal few-outcome SLD readout admits a dimension-free central-plus-tail bound, is stable under Wasserstein-2 perturbations of the state-weighted score measure, has a dense-spectrum high-rate quantization window, and crosses exactly to zero distortion once the bin count reaches the finite score-support size.
RO-2026-0001:C2
claimFor a rank-one projective measurement, the quantum-Fisher loss equals the rho-weighted squared residual between its induced score operator and the SLD, providing an exact projective-search stopping certificate; the broader local-to-global and pair-rotation geometry is an imported companion result.
RO-2026-0001:C3
claimFor an actual parameter-independent initialized isometry V with exhaustive ordinary, boundary, leakage, and failure labels, a bounded label-score observable C, and an approximate Hermitian SLD L-tilde, the uniform score-intertwining defect xi = norm(CV - V L-tilde) controls the actual POVM Fisher loss by (eta + xi)^2. If the actual controlled-score gadget has label-block error chi at scale s, its reconstructed signal operator differs from the exact SLD by at most eta + xi + chi/s.
RO-2026-0001:C4
claimProducing a coherent SLD score instrument that satisfies the declared score-intertwining and signal-block interface at inverse-polynomial accuracy is BQP-hard for a faithful, trace-normalized, full-support metrological embedding with polynomial state conditioning, inverse-polynomial zero-score margin, inverse-polynomial quantum Fisher information, and inverse-polynomial coherent application success, even though the sensor-state score histogram is independent of the encoded linear-system right-hand side.
RO-2026-0001:C5
claimThe parity-coherence sensing family has constant condition number three, quantum Fisher information n divided by four, exactly n plus one SLD scores, and logarithmic score-register size, while Gibbs access obeys the rescaling-invariant conditioning obstruction exp(beta times energy span) and the archived finite-size beta proportional to one over n family has bounded conditioning together with the reported rescaled sensitivity.
RO-2026-0001:C6
claimIn the archived frustrated four-spin sensor benchmark, the best product projective readout found by the archived heuristic search retains 48.55 percent of the quantum Fisher information, whereas globally optimized contiguous seven- and eight-bin SLD score readouts retain 98.34 percent and 99.26 percent respectively.
RO-2026-0001:C7
evidencedata/gap_identity.csv
RO-2026-0001:evidence:data/gap_identity.csv
evidencedata/gibbs_conditioning.csv
RO-2026-0001:evidence:data/gibbs_conditioning.csv
evidencedata/hardness_reduction.csv
RO-2026-0001:evidence:data/hardness_reduction.csv
evidencedata/parity_sensor.csv
RO-2026-0001:evidence:data/parity_sensor.csv
evidencedata/physical_chain.csv
RO-2026-0001:evidence:data/physical_chain.csv
evidencedata/physical_product_parameters.npy
RO-2026-0001:evidence:data/physical_product_parameters.npy
evidencedata/physical_resolution.csv
RO-2026-0001:evidence:data/physical_resolution.csv
evidencedata/resolution_raw.csv
RO-2026-0001:evidence:data/resolution_raw.csv
evidencedata/resolution_summary.csv
RO-2026-0001:evidence:data/resolution_summary.csv
evidencedata/resource_estimate.json
RO-2026-0001:evidence:data/resource_estimate.json
evidencedata/resource_operators.csv
RO-2026-0001:evidence:data/resource_operators.csv
evidencedata/saddle_landscape.npz
RO-2026-0001:evidence:data/saddle_landscape.npz
evidencedata/score_compression.csv
RO-2026-0001:evidence:data/score_compression.csv
evidencedata/tail_bound.csv
RO-2026-0001:evidence:data/tail_bound.csv
evidencedata/thermodynamic_quantization.csv
RO-2026-0001:evidence:data/thermodynamic_quantization.csv
evidencefigures/figure3.pdf
RO-2026-0001:evidence:figures/figure3.pdf
evidencesrc/appendices.tex
RO-2026-0001:evidence:src/appendices.tex
evidencesrc/references.bib
RO-2026-0001:evidence:src/references.bib
evidencesrc/sections/03-compression.tex
RO-2026-0001:evidence:src/sections/03-compression.tex
evidencesrc/sections/03-landscape.tex
RO-2026-0001:evidence:src/sections/03-landscape.tex
evidencesrc/sections/05-compiler.tex
RO-2026-0001:evidence:src/sections/05-compiler.tex
evidencesrc/sections/06-hardness.tex
RO-2026-0001:evidence:src/sections/06-hardness.tex
evidencesrc/sections/07-numerics.tex
RO-2026-0001:evidence:src/sections/07-numerics.tex
evidencesrc/sections/08-physical.tex
RO-2026-0001:evidence:src/sections/08-physical.tex
programMathematical Physics
PRG-mathematical-physics
programQuantum Information
PRG-quantum-information
programQuantum Thermodynamics
PRG-quantum-thermodynamics
research objectFew-Outcome Readout of Quantum-Fisher-Optimal Measurements: Sharp Bounds and Coherent-Synthesis Hardness
RO-2026-0001
sourcesrc/qsa_core.py
code:src/qsa_core.py
sourcesrc/simulate.py
code:src/simulate.py
sourcedata/physical_chain.csv
dataset:data/physical_chain.csv
sourceBenign-Projective-Landscapes-for-Measured-Quantum-Divergences
external_result:Benign-Projective-Landscapes-for-Measured-Quantum-Divergences
sourceBQP-hard-quantum-linear-systems
external_result:BQP-hard-quantum-linear-systems
sourceCable-Gu-Modi-2016-one-clean-qubit-metrology
external_result:Cable-Gu-Modi-2016-one-clean-qubit-metrology
sourceGraf-Luschgy-2000-Theorem-6.2
external_result:Graf-Luschgy-2000-Theorem-6.2
sourceLiu-Pages-2020-Wasserstein-root-distortion
external_result:Liu-Pages-2020-Wasserstein-root-distortion
sourcequantum-Sylvester-solver
external_result:quantum-Sylvester-solver
sourcequbitization-and-quantum-signal-processing
external_result:qubitization-and-quantum-signal-processing
sourcescalar-quantization-high-rate-theory
external_result:scalar-quantization-high-rate-theory
sourceSheng-2026-Stinespring-score-intertwining-QFI-loss
external_result:Sheng-2026-Stinespring-score-intertwining-QFI-loss
sourceSheng-2026-task-dependent-syndrome-memory
external_result:Sheng-2026-task-dependent-syndrome-memory
storyWhy a Quantum Detector Might Need Fewer Answers
STORY-2026-0001
taxonomyBlock encoding
method:block-encoding
taxonomyIndependent reproduction
method:independent-reproduction
taxonomyLiterature audit
method:literature-audit
taxonomyNumerical validation
method:numerical-validation
taxonomyProof construction
method:proof-construction
taxonomyScore quantization
method:score-quantization
taxonomyMathematical physics
subject:mathematical-physics
taxonomyQuantum computational complexity
subject:quantum-complexity
taxonomyQuantum information
subject:quantum-information
taxonomyQuantum measurement
subject:quantum-measurement
taxonomyQuantum metrology
subject:quantum-metrology
taxonomyQuantum thermodynamics
subject:quantum-thermodynamics
taxonomyOpen quantum systems
system:open-quantum-systems
taxonomyQuantum sensors
system:quantum-sensors
taxonomyQubit spin systems
system:qubit-spin-systems