trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Projection Probability Flow

Finite-dimensional Hamiltonian evolution differentiates projection probabilities by the commutator trace and conserves them for commuting projections.

Closed Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES22
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Projection probabilities follow the commutator trace

RELATIONSHIP ATLAS

Every connection, in context.

Explore in 3D
Direct recorded relationships
Projected Unitary DynamicsProjected Unitary DynamicsQuantum Relative-Entropy Defect CompositionQuantum Relative-Entropy DefectCompositionFinite-Dimensional Quantum SkeletonsFinite-Dimensional QuantumSkeletonsProjection Probability FlowProjection Probability FlowInfinitesimal Reducing CriterionInfinitesimal ReducingCriterionAnalytic Flow GenerationAnalytic Flow GenerationA 23-edge coupling realizes the ten-mode Fourier transformA 23-edge coupling realizes theten-mode Fourier transformConservation And Autonomy Are DistinctConservation And Autonomy AreDistinctEntropy Production by Coherence DeletionEntropy Production by CoherenceDeletionInfinitely many non-star trees admit Laplacian peak state transferInfinitely many non-star treesadmit Laplacian peak statetransferA genuine four-state superposition from level-one QAOAA genuine four-statesuperposition from level-oneQAOASong and Lin's parity conjecture for zero transfer is falseSong and Lin's parityconjecture for zero transfer isfalsePretty good state transfer at vertex 4 of the double blow-up of P_11Pretty good state transfer atvertex 4 of the double blow-upof P_11The twin end vertex of P'_9 is not sharply 1/9-sedentaryThe twin end vertex of P'_9 isnot sharply 1/9-sedentaryPolygonal couplings and the discrete Fourier transformPolygonal couplings and thediscrete Fourier transformPositive Pauli Clock OrderPositive Pauli Clock OrderA property-T circulant with universal perfect state transferA property-T circulant withuniversal perfect statetransferNo perfect state transfer at time pi on rational paths with 2^k + 1 verticesNo perfect state transfer attime pi on rational paths with2^k + 1 verticesEarly state exclusion in seven-site transfer chains with symmetric spectrumEarly state exclusion in seven-site transfer chains withsymmetric spectrumSubsystem Lanczos positivity failsSubsystem Lanczos positivityfailsSpectrum and first-site amplitude of seven-site transfer chains with symmetric spectrumSpectrum and first-siteamplitude of seven-sitetransfer chains with symmetricOrder-three Renyi information combiningOrder-three Renyi informationcombiningA counterexample to Zhang–Wu–Fei superadditivityA counterexample toZhang–Wu–Fei superadditivityBoundary Rényi magic additivityBoundary Rényi magic additivityThe sharp Hoggar-SIC sum negativityThe sharp Hoggar-SIC sumnegativityThe Free-Negentropy BudgetThe Free-Negentropy Budget
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

RELATED KNOWLEDGE

Structural connections

Documents & exposition

Other authored & advisory relationships

None recorded in this release.

LIBRARY / RELEASE VERSIONS

Content history

Loading release versions...
Browse the archive

Certified provenance

Exact release coordinate

Authority boundary

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.