Quantum / CONCEPT
Cartesian variance
A pure vector maximizes the Cartesian matrix variance.
Closed
DIRECT PREREQUISITES5
DIRECT CONSEQUENCES23
PROOF DEPTH6
DOCUMENT LINKS0
Density matrices exist in positive dimension
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A supporting functional at every pure bipartite statetruth-dependency · Closed
- AbsoluteTwoIncoherencePurityRefutationtruth-dependency · Closed
- Commutator gap and scalar translationtruth-dependency · Closed
- Entangled inputs violate output maximal coherence tensorizationtruth-dependency · Closed
- Entropy under entrywise modulus in dimension threetruth-dependency · Closed
- Error and disturbance below the endpoint minimumtruth-dependency · Closed
- FactorWidthTwoConetruth-dependency · Closed
- Formation is not constant on the three-vector subspacetruth-dependency · Closed
- Generalized Choi maps and absolute PPTtruth-dependency · Closed
- IncoherentConetruth-dependency · Closed
- Optimal visibility for calibrated joint measurementstruth-dependency · Closed
- OverlapLowRankDistancetruth-dependency · Closed
- Positive Branch Reachability and Responsetruth-dependency · Closed
- QubitWassersteinCouplingstruth-dependency · Closed
- Radial convexity and endpoint derivativestruth-dependency · Closed
- Rico–Życzkowski nonlinear monotone refutationtruth-dependency · Closed
- Schmidt-number bounds for incomplete equiangular measurementstruth-dependency · Closed
- Schur–Frobenius inequality and equalitytruth-dependency · Closed
- The diagonal difference boundtruth-dependency · Closed
- The sharp odd-prime unentangled communication boundtruth-dependency · Closed
- WassersteinComplexityNonconvextruth-dependency · Closed
- Weak products do not preserve edge-complexity equalitytruth-dependency · Closed
- Zero diagonal blockstruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A counterexample to Lin's Conjecture 4.3structural-affinity · Closed
- A counterexample to the radial convexity characterizationstructural-affinity · Closed
- A supporting functional at every pure bipartite statestructural-affinity · Closed
- AbsoluteTwoIncoherencePurityRefutationstructural-affinity · Closed
- Bourin–Lee Conjecture 3.3structural-affinity · Closed
- Coherent discrimination bias is not a channel metricstructural-affinity · Closed
- Commutator gap and scalar translationstructural-affinity · Closed
- Compact Convex Readout Fibersstructural-affinity · Closed
- Entangled inputs violate output maximal coherence tensorizationstructural-affinity · Closed
- Entropy under entrywise modulus in dimension threestructural-affinity · Closed
- Equal Gram Unitary Extensionstructural-affinity · Closed
- Error and disturbance below the endpoint minimumstructural-affinity · Closed
- FactorWidthTwoConestructural-affinity · Closed
- Finite-Dimensional Physical Fiberstructural-affinity · Closed
- Formation is not constant on the three-vector subspacestructural-affinity · Closed
- Generalized Choi maps and absolute PPTstructural-affinity · Closed
- IncoherentConestructural-affinity · Closed
- Infinitesimal Reducing Criterionstructural-affinity · Closed
- Numerical ranges and compressionstructural-affinity · Closed
- Optimal visibility for calibrated joint measurementsstructural-affinity · Closed
- OverlapLowRankDistancestructural-affinity · Closed
- Positive Branch Reachability and Responsestructural-affinity · Closed
- Positivity at both endpointsstructural-affinity · Closed
- Projection Commutator Identitystructural-affinity · Closed
- Quantitative edges of a positive and negative block spikestructural-affinity · Closed
- Radial convexity and endpoint derivativesstructural-affinity · Closed
- Residual-Driven Projective Energystructural-affinity · Closed
- Resolvent derivatives and radial distancestructural-affinity · Closed
- Rico–Życzkowski nonlinear monotone refutationstructural-affinity · Closed
- Schur–Frobenius inequality and equalitystructural-affinity · Closed
- Semi-nonnegative maps can exhibit information backflowstructural-affinity · Closed
- Tang–Zhang's sharp order −2 inequalitystructural-affinity · Closed
- The 2-neighbour bootstrap percolation number of C_n x P_m is nstructural-affinity · Closed
- The diagonal difference boundstructural-affinity · Closed
- The normalized geometric-mean comparisonstructural-affinity · Closed
- The rational functional-calculus expressionstructural-affinity · Closed
- The sharp odd-prime unentangled communication boundstructural-affinity · Closed
- The sharp spectral moment inequalitystructural-affinity · Closed
- Unambiguous discrimination without repeated labelsstructural-affinity · Closed
- Universal Replacement Capacity Growthstructural-affinity · Closed
- Visible-Hidden Projection Criteriastructural-affinity · Closed
- WassersteinComplexityNonconvexstructural-affinity · Closed
- Weak products do not preserve edge-complexity equalitystructural-affinity · Closed
- Weighted Bottcher-Wenzel, case (ii)structural-affinity · Closed
- Zero diagonal blocksstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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