Quantum / CONCEPT
The separable numerical range of one two-qubit observable
For a single two-qubit observable A, the length of the separable numerical range is at least half the length of the numerical range, and the projector onto (|00> + |11>)/sqrt(2) attains one half. This proves Conjecture 8 of T. Simnacher, J. Czartowski, K. Szymański and K. Życzkowski (arXiv:2107.04365): the minimal volume ratio mu_{2,1} equals 1/2.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS0
Zero determinant gives a product vector
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
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Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Binegativity is not monotone under one-way LOCCstructural-affinity · Closed
- Canonical Separable Cone Residualstructural-affinity · Closed
- Negativity and structured negativity differ for a pure two-qutrit statestructural-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
- The Strict Composite Matrix-Cone Chainstructural-affinity · Closed
- The two-qubit binegativity lower bound at fixed negativitystructural-affinity · Closed
- The upper binegativity bound of Girard and Gour failsstructural-affinity · Closed
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