Quantum / CONCEPT
The forbidden-subgraph conjecture for MMI in graph states
Every graph state that violates monogamy of mutual information is carried by local complementations to a graph with an induced four-star, and that graph is a generalized star for the partition that places the three leaves of the star in their own parts and every other vertex in the centre. This proves the forbidden-subgraph conjecture of Fuentes, Keeler, Munizzi and Pollack for every number of qubits.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES2
PROOF DEPTH0
DOCUMENT LINKS0
Entropy of the complement
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
RELATED KNOWLEDGE
Structural connections
- A product decomposition of the generalized CHSH groupsstructural-affinity · Closed
- Components and Vertex Cutsstructural-affinity · Closed
- Condensation need not preserve LC-equivalencestructural-affinity · Closed
- Connected encoder classes and powers of threestructural-affinity · Closed
- Equivalence of bipartite encoder formsstructural-affinity · Closed
- Reconstruction from even-legged hyperlinksstructural-affinity · Closed
Documents & exposition
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Other authored & advisory relationships
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