Quantum / CONCEPT
The least trace-distance contraction coefficient over a classical channel
A qubit channel lies over a classical channel when the images of the two basis projections have the prescribed diagonal entries. Over the classical channel with parameters a and f, the trace-distance contraction coefficient of every such qubit channel is at least |a - f|, and a measure-and-prepare channel attains this value.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH2
DOCUMENT LINKS1
The infimum is |a - f| and is attained
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
- Centered Kraus trace norm on finite referencesstructural-affinity · Closed
- Comparability of conical-design concurrence boundsstructural-affinity · Closed
- Cyclic Refractory Quantum Generatorstructural-affinity · Closed
- Finite Kraus Quantum Channelsstructural-affinity · Closed
- Finite Kraus Representationsstructural-affinity · Closed
- Finite Record Cosine Obstructionstructural-affinity · Closed
- Finite Record Recovery Errorstructural-affinity · Closed
- Finite Reference Channel Distancestructural-affinity · Closed
- Finite Trace Distancestructural-affinity · Closed
- FinitePreparationChannelstructural-affinity · Closed
- Negativity is not the partial transpose distance to the PPT statesstructural-affinity · Closed
- Pure targets prevent general square-root savingsstructural-affinity · Closed
- Real rectangular nuclear-norm additivitystructural-affinity · Closed
- The overlap-to-purity part of Kopel's equality theoremstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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