Resource / CONCEPT
The Inclusion Chain of Composite Matrix Cones
For finite complex matrices, separable, positive-semidefinite, and block-positive cones form a proved inclusion chain.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES6
PROOF DEPTH0
DOCUMENT LINKS1
Separable matrices are positive semidefinite
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
- Advantage-quantum measurements cannot be simulated with finitely many copiestruth-dependency · Closed
- Properness of the Composite Matrix-Cone Inclusionstruth-dependency · Closed
- Resource: Composite Cone Dualitytruth-dependency · Closed
- Resource: Entanglement Witnesstruth-dependency · Closed
- Resource: Entanglement Witness Existstruth-dependency · Closed
- Resource: Separable Cone Closedtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Advantage-quantum measurements cannot be simulated with finitely many copiesstructural-affinity · Closed
- Canonical Separable Cone Residualstructural-affinity · Closed
- Contraction decompositions and separable scalar shiftsstructural-affinity · Closed
- Properness of the Composite Matrix-Cone Inclusionsstructural-affinity · Closed
- Resource: Composite Cone Dualitystructural-affinity · Closed
- Resource: Entanglement Witnessstructural-affinity · Closed
- Resource: Entanglement Witness Existsstructural-affinity · Closed
- Resource: Separable Cone Closedstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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