Quantum / CONCEPT
The upper binegativity bound of Girard and Gour fails
Girard and Gour (arXiv:1701.02724) conjecture that the binegativity of every two-qubit state is at most nu (c + nu)^2 / (2 (c^2 + nu^2)), where nu is the negativity and c the concurrence. The upper bound fails: the rank-two state (|v><v| + 9 |00><00|)/26 with v = (3, 2, 2, 0) has negativity 2/13, concurrence at least 4/13 and binegativity 1/7, while the bound is at most 9/65.
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The upper bound fails
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Proof dependencyStructural affinityDocument link
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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
- Negativity and structured negativity differ for a pure two-qutrit statestructural-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
- The separable numerical range of one two-qubit observablestructural-affinity · Closed
- The two-qubit binegativity lower bound at fixed negativitystructural-affinity · Closed
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