trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Finite Density Purification

A finite density state has a canonical normalized purification with exact reduced marginal.

Closed Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES7
PROOF DEPTH17
DOCUMENT LINKS0

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Finite Density States and Quantum ChannelsFinite Density States andQuantum ChannelsPartial Trace and Quantum Mutual InformationPartial Trace and QuantumMutual InformationQuantum: M StateQuantum: M StateFinite Density PurificationFinite Density PurificationOrthogonal reduction for conditional hockey-stick ratiosOrthogonal reduction forconditional hockey-stick ratiosFailure of partial-negativity subadditivityFailure of partial-negativitysubadditivitySchmidt-number bounds for incomplete equiangular measurementsSchmidt-number bounds forincomplete equiangularmeasurementsThe qutrit overlap entropy bound is unattainableThe qutrit overlap entropybound is unattainableActual Density Strong SubadditivityActual Density StrongSubadditivityBound coherence in every dimension at least threeBound coherence in everydimension at least threeA replacement channel and the Schumacher-Westmoreland constructionA replacement channel and theSchumacher-Westmorelandconstruction
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Lean sourceResearch workspace
Status
Closed
Depth
17
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Foundation/FiniteDensityPurification
Repository path
D5/S3/Quantum/Foundation/FiniteDensityPurification.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.