Quantum / CONCEPT
The fully entangled fraction and the steering-ellipsoid centre
Every two-qubit density matrix rho satisfies rho <= (2 - |c|)(1 tensor rho_B), where c is the centre of Alice's steering ellipsoid and rho_B is Bob's reduced state; hence its fully entangled fraction is at most 1 - |c|/2, and every value |c| = t in [0, 1] is attained by a state whose fully entangled fraction equals 1 - t/2. This proves Conjecture 2 of A. Milne, D. Jennings, S. Jevtic and T. Rudolph (arXiv:1404.3951).
Closed
DIRECT PREREQUISITES6
DIRECT CONSEQUENCES5
PROOF DEPTH19
DOCUMENT LINKS0
The first Pauli matrix
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
- A Tight CHSH Witnesstruth-dependency · Closed
- Finite-Dimensional Quantum Skeletonstruth-dependency · Closed
- Local-unitary inequivalence of two weight-isometric pairs of stabilizer codestruth-dependency · Closed
- Orthogonal reduction for conditional hockey-stick ratiostruth-dependency · Closed
- Partial Trace and Quantum Mutual Informationtruth-dependency · Closed
- Pure-qubit affine geometrytruth-dependency · Closed
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A qudit counterexample to genuine entropic tetrahedrastructural-affinity · Closed
- A Tight CHSH Witnessstructural-affinity · Closed
- ChannelTimeReversalNoGostructural-affinity · Closed
- Finite-Dimensional Quantum Skeletonsstructural-affinity · Closed
- Four MUBs refute the dimension-eight necessity boundstructural-affinity · Closed
- Geometric discord and maximal mutual correlationstructural-affinity · Closed
- Orthogonal reduction for conditional hockey-stick ratiosstructural-affinity · Closed
- Partial Trace and Quantum Mutual Informationstructural-affinity · Closed
- QubitWassersteinCouplingsstructural-affinity · Closed
- Robustness of ancilla-free testersstructural-affinity · Closed
- Subsystem Lanczos positivity failsstructural-affinity · Closed
- The balanced-cut gradient bound fails for eight qubitsstructural-affinity · Closed
- The purification lower bound fails for a qutritstructural-affinity · Closed
- The steering-ellipsoid CHSH boundstructural-affinity · Closed
- WassersteinComplexityNonconvexstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance