trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Matrix GNS Identity

Positive trace-one matrix weights are Hilbert-Schmidt norm squares.

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DIRECT PREREQUISITES0
DIRECT CONSEQUENCES13
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DOCUMENT LINKS1
THEOREM

Positive matrix weights are Hilbert-Schmidt norm squares

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Matrix GNS IdentityMatrix GNS IdentityRoot Fidelity and Binary PreparationRoot Fidelity and BinaryPreparationOrdered Three-Pulse TraceOrdered Three-Pulse TraceThe Gurvits--Barnum separable ballThe Gurvits--Barnum separableballSchmidt-number bounds for incomplete equiangular measurementsSchmidt-number bounds forincomplete equiangularmeasurementsCommutator gap and scalar translationCommutator gap and scalartranslationMatrix Self-PairingMatrix Self-PairingConcatenation can increase the cHaar moment normConcatenation can increase thecHaar moment normFour-path weighted equality remainderFour-path weighted equalityremainderA positive map reflecting positive contractionsA positive map reflectingpositive contractionsMixed-State Robertson UncertaintyMixed-State RobertsonUncertaintyMatrix-State Cone SectionsMatrix-State Cone SectionsZero Norm Propagation for Matrix StatesZero Norm Propagation forMatrix StatesTang–Zhang's sharp order −2 inequalityTang–Zhang's sharp order −2inequality
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/GNSMatrix
Repository path
D5/S3/Quantum/GNSMatrix.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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