trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Quantum Relative-Entropy Defect Composition

Quantum relative-entropy loss telescopes along composable matrix channels.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES15
PROOF DEPTH1
DOCUMENT LINKS0
THEOREM

Quantum relative-entropy defects form an additive channel chain

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Invariant States of Finite-Dimensional ChannelsInvariant States of Finite-Dimensional ChannelsQuantum Relative-Entropy Defect CompositionQuantum Relative-Entropy DefectCompositionTyped Prime-Language HierarchyTyped Prime-Language HierarchyLegacy Relative-Entropy BoundaryLegacy Relative-EntropyBoundaryVon Neumann Entropy Under Basis PinchingVon Neumann Entropy Under BasisPinchingProjection Probability FlowProjection Probability FlowLocal Observation Partial-Trace EquivalenceLocal Observation Partial-TraceEquivalenceFuture Statistics and the Infinite Operator SystemFuture Statistics and theInfinite Operator SystemRefutation of completely contractive CMI data processingRefutation of completelycontractive CMI data processingDensity-state covariance and its sparse sumDensity-state covariance andits sparse sumA counterexample to Zhang–Wu–Fei superadditivityA counterexample toZhang–Wu–Fei superadditivityFinite Kraus Instrument Born MarginalFinite Kraus Instrument BornMarginalWord-Probability Trace RepresentationWord-Probability TraceRepresentationFinite Prime-Time CertificateFinite Prime-Time CertificateA strong-subadditivity counterexample for subentropyA strong-subadditivitycounterexample for subentropyInformational Completeness EquivalenceInformational CompletenessEquivalenceMixed-State Robertson UncertaintyMixed-State RobertsonUncertainty
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Divergence/QuantumRelativeEntropyDefectComposition
Repository path
D5/S3/Quantum/Divergence/QuantumRelativeEntropyDefectComposition.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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