trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Finite Sector Channel Optimality

The common residual spectra determine the exact channel error for sector coarse-graining under arbitrary local quantum operations and finite shared classical mixtures.

Closed Authored exposition
DIRECT PREREQUISITES14
DIRECT CONSEQUENCES1
PROOF DEPTH8
DOCUMENT LINKS1
THEOREM

The residual Gram minimum determines the optimum

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Finite Moore-Penrose InverseFinite Moore-Penrose InverseFinite Sector Channel ModelFinite Sector Channel ModelFlat Sector Rank FeasibilityFlat Sector Rank FeasibilityPassive Sector-Pair BoundPassive Sector-Pair BoundPhysical Sector Channel ConstructionPhysical Sector ChannelConstructionRectangular Variational BoundRectangular Variational BoundSchur Channel Upper BoundSchur Channel Upper BoundSector Schmidt EncodingsSector Schmidt EncodingsFinite Reference Channel DistanceFinite Reference ChannelDistanceFinite Kraus Quantum ChannelsFinite Kraus Quantum ChannelsFinite Density States and Quantum ChannelsFinite Density States andQuantum ChannelsFinite Trace DistanceFinite Trace DistancePartial Trace and Quantum Mutual InformationPartial Trace and QuantumMutual InformationWeil: SylvesterWeil: SylvesterFinite Sector Channel OptimalityFinite Sector ChannelOptimalityCompact Flat Sector OptimumCompact Flat Sector Optimum
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Lean sourceResearch workspace
Status
Closed
Depth
8
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Entanglement/FiniteSectorChannelOptimality
Repository path
D5/S3/Quantum/Entanglement/FiniteSectorChannelOptimality.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
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.