Quantum / CONCEPT
Negativity and structured negativity differ for a pure two-qutrit state
The pure state (|00⟩ + 2|11⟩ + 2|22⟩)/3 has three negative partial-transpose eigenvalues, but negativity 8/9 and structured negativity 4/3. It refutes the coincidence conjecture of Kumari and Adhikari.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES12
PROOF DEPTH0
DOCUMENT LINKS1
Refutation by a pure 3⊗3 state
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
- A generic-state counterexample in the kicked Ising chaintruth-dependency · Closed
- ConstructionReductiontruth-dependency · Closed
- FormationBoundstruth-dependency · Closed
- Four MUBs refute the dimension-eight necessity boundtruth-dependency · Closed
- Negativity is not the partial transpose distance to the PPT statestruth-dependency · Closed
- Noisy entanglement curvature can exceed quantum Fisher informationtruth-dependency · Closed
- Pairwise and joint entanglement detectiontruth-dependency · Closed
- Passive memory with a nonclassical Gram matrixtruth-dependency · Closed
- Separable states outside every local-unitary stabilizer frametruth-dependency · Closed
- Steering does not force atemporalitytruth-dependency · Closed
- The separable numerical range of one two-qubit observabletruth-dependency · Closed
- The upper binegativity bound of Girard and Gour failstruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A generic-state counterexample in the kicked Ising chainstructural-affinity · Closed
- Binegativity is not monotone under one-way LOCCstructural-affinity · Closed
- ConstructionReductionstructural-affinity · Closed
- FormationBoundsstructural-affinity · Closed
- Four MUBs refute the dimension-eight necessity boundstructural-affinity · Closed
- Negativity is not the partial transpose distance to the PPT statesstructural-affinity · Closed
- Noisy entanglement curvature can exceed quantum Fisher informationstructural-affinity · Closed
- Pairwise and joint entanglement detectionstructural-affinity · Closed
- Passive memory with a nonclassical Gram matrixstructural-affinity · Closed
- Separable states outside every local-unitary stabilizer framestructural-affinity · Closed
- Steering does not force atemporalitystructural-affinity · Closed
- The separable numerical range of one two-qubit observablestructural-affinity · Closed
- The upper binegativity bound of Girard and Gour failsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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