trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Separable states outside every local-unitary stabilizer frame

A rank-two mixture of two nonorthogonal product states remains outside the full convex stabilizer hull under every local unitary.

Closed Authored exposition
DIRECT PREREQUISITES9
DIRECT CONSEQUENCES11
PROOF DEPTH19
DOCUMENT LINKS0
THEOREM

Unitary matrices preserve overlaps

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Negativity and structured negativity differ for a pure two-qutrit stateNegativity and structurednegativity differ for a puretwo-qutrit stateSchmidt-number bounds for incomplete equiangular measurementsSchmidt-number bounds forincomplete equiangularmeasurementsPartial Trace and Quantum Mutual InformationPartial Trace and QuantumMutual InformationThe signed Pauli sum bound fails for three qubitsThe signed Pauli sum boundfails for three qubitsWigner distance minimum attainmentWigner distance minimumattainmentOccupationPartialTransposeSpectralOccupationPartialTransposeSpectralThe Pure-State HandshakeThe Pure-State HandshakeThe overlap-to-purity part of Kopel's equality theoremThe overlap-to-purity part ofKopel's equality theoremFiniteLocalLatitudeGeometryFiniteLocalLatitudeGeometrySeparable states outside every local-unitary stabilizer frameSeparable states outside everylocal-unitary stabilizer frameFormationBoundsFormationBoundsSelectiveFormationBoundsSelectiveFormationBoundsLocal distinguishability at boundary projection statesLocal distinguishability atboundary projection statesCommuting encodings and local reflectionsCommuting encodings and localreflectionsMulti-entropy positivity fails on three qutritsMulti-entropy positivity failson three qutritsPartial tightness of the multipartite entangled-measurement boundPartial tightness of themultipartite entangled-measurement boundLog-negativity capacity depends on the input resourceLog-negativity capacity dependson the input resourceOne ancillary qubit cannot give constant-round universal channel simulationOne ancillary qubit cannot giveconstant-round universalchannel simulationBayesian feedback advantage for the qutrit Werner–Holevo channelBayesian feedback advantage forthe qutrit Werner–HolevochannelCoherence damping fails for complex hoppingCoherence damping fails forcomplex hoppingDeterministic violations under an energy constraintDeterministic violations underan energy constraint
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
19
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Information/SeparableStateLocalUnitaryStabilizerObstruction
Repository path
D5/S3/Quantum/Information/SeparableStateLocalUnitaryStabilizerObstruction.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.