trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

The Pure-State Handshake

A pure state sandwiches any matrix to a scalar multiple of itself.

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DIRECT PREREQUISITES0
DIRECT CONSEQUENCES30
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THEOREM

The pure-state sandwich collapses to a scalar

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The Pure-State HandshakeThe Pure-State HandshakeA triangle inequality fails for unified-entropy correlationsA triangle inequality fails forunified-entropy correlationsThermofield Marginal and Modular SpectrumThermofield Marginal andModular SpectrumEmpirical and Reflexive Completeness SeparateEmpirical and ReflexiveCompleteness SeparateTwo unbounded entanglement gaps with one qubitTwo unbounded entanglement gapswith one qubitRegularity of the qudit CHSH graphRegularity of the qudit CHSHgraphEnergy eigenstates have no changing density recordEnergy eigenstates have nochanging density recordSubsystem Lanczos positivity failsSubsystem Lanczos positivityfailsA Pure Bell State with a Mixed MarginalA Pure Bell State with a MixedMarginalFormationBoundsFormationBoundsM-resistant qudit states exist in every admissible rangeM-resistant qudit states existin every admissible rangeSelective LOCC can increase the Moreau-Yosida entanglement of formationSelective LOCC can increase theMoreau-Yosida entanglement offormationSchmidt-number bounds for incomplete equiangular measurementsSchmidt-number bounds forincomplete equiangularmeasurementsThe two-qubit binegativity lower bound at fixed negativityThe two-qubit binegativitylower bound at fixed negativityRefuting the density-tensor nuclear-norm equality conjectureRefuting the density-tensornuclear-norm equalityconjectureEqual coherence roofs on a mixed rank-two stateEqual coherence roofs on amixed rank-two statePurify-and-clone is not optimal for one-site worst-case riskPurify-and-clone is not optimalfor one-site worst-case riskA lower bound on qutrit magic from coherenceA lower bound on qutrit magicfrom coherenceSeparable states outside every local-unitary stabilizer frameSeparable states outside everylocal-unitary stabilizer frameTemporal Schatten subadditivity is falseTemporal Schatten subadditivityis falseAntidistinguishabilityOverlapNonTightAntidistinguishabilityOverlapNonTightExact Conditional Preparation CostExact Conditional PreparationCostOriginal Single-Terminal Ternary ObstructionOriginal Single-TerminalTernary ObstructionA stabilizer measurement beyond every maximally entangled oneA stabilizer measurement beyondevery maximally entangled oneBroadcasting channels need have neither extremumBroadcasting channels need haveneither extremumThe three-distinguishability product conjecture failsThe three-distinguishabilityproduct conjecture failsA qubit pure-program obstructionA qubit pure-programobstructionQubitWassersteinCouplingsQubitWassersteinCouplingsPauli-weight expansion and alternating truncation bounds for qubit SIC k-fidelitiesPauli-weight expansion andalternating truncation boundsfor qubit SIC k-fidelitiesBinomial and kappa states do not exhaust truncated entropy minimizersBinomial and kappa states donot exhaust truncated entropyminimizersNegativity does not imply positive reductionNegativity does not implypositive reduction
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/PureState/PureStateHandshake
Repository path
D5/S3/Quantum/PureState/PureStateHandshake.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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