trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

The three-state root-fidelity Holevo bound

Root-fidelity matrix entropy bounds the Holevo quantity of every three-state ensemble.

Closed Authored exposition
DIRECT PREREQUISITES19
DIRECT CONSEQUENCES0
PROOF DEPTH9
DOCUMENT LINKS0
THEOREM

The Holevo bound for three arbitrary states

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Canonical Quantum Channel Data ProcessingCanonical Quantum Channel DataProcessingActual relative modular modelActual relative modular modelSupport-Aware Quantum Relative EntropySupport-Aware Quantum RelativeEntropyEntropy under entrywise modulus in dimension threeEntropy under entrywise modulusin dimension threeEntropy Production by Coherence DeletionEntropy Production by CoherenceDeletionConstructionReductionConstructionReductionUniversal Replacement Capacity GrowthUniversal Replacement CapacityGrowthRecord Fixed Algebra DecompositionRecord Fixed AlgebraDecompositionFinite Kraus Quantum ChannelsFinite Kraus Quantum ChannelsFinite Density States and Quantum ChannelsFinite Density States andQuantum ChannelsFinite Trace DistanceFinite Trace DistanceRefutation of completely contractive CMI data processingRefutation of completelycontractive CMI data processingStrict separation of measured and Uhlmann average fidelitiesStrict separation of measuredand Uhlmann average fidelitiesPartial Trace and Quantum Mutual InformationPartial Trace and QuantumMutual InformationOccupationPartialTransposeSpectralOccupationPartialTransposeSpectralPurifiedLocalPathPurifiedLocalPathThe trace norm and its two-dimensional formulaThe trace norm and its two-dimensional formulaUnitarily invariant norms and symmetric diagonal gaugesUnitarily invariant norms andsymmetric diagonal gaugesUnitary spectral blocks and the tensor boundUnitary spectral blocks and thetensor boundThe three-state root-fidelity Holevo boundThe three-state root-fidelityHolevo bound
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Lean sourceResearch workspace
Status
Closed
Depth
9
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Divergence/FannesRootFidelityHolevo
Repository path
D5/S3/Quantum/Divergence/FannesRootFidelityHolevo.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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