Quantum / CONCEPT
Fixed-Pair Convexity of Generalized Fidelity
For a fixed positive definite qubit reference R and a second input Q of trace one, the squared generalized Bures--Wasserstein quantity is convex in its first density-state input exactly when its Hermitian square-root coefficient is positive semidefinite.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH5
DOCUMENT LINKS0
The exact positivity criterion
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- Clifford Path Realizationsstructural-affinity · Closed
- Commuting Qubit Midpoint Contractionstructural-affinity · Closed
- Conditioning Trace-Distance Constantstructural-affinity · Closed
- Exact Conditional Preparation Coststructural-affinity · Closed
- Ordered GNS Projectionsstructural-affinity · Closed
- Qubit Generalized Fidelity and Failure of Data Processingstructural-affinity · Closed
- Root Fidelity and Binary Preparationstructural-affinity · Closed
- Tightness of the Fixed CHSH Witnessstructural-affinity · Closed
- TwoPositiveTransitionTracestructural-affinity · Closed
- Weil: Rank Tracestructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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