Quantum / CONCEPT
A qutrit obstruction to positive/CP factorization of the channel transpose
A unital qutrit measure-and-prepare channel has no factorization of its channel transpose through a positive outer filter and a completely positive inner filter. Nonnegative coefficients impose kernel constraints incompatible with the unital sum and the nonorthogonal state kernels.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES12
PROOF DEPTH4
DOCUMENT LINKS1
Complete positivity implies positivity
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A non-extreme minimum-rank superchannel extensiontruth-dependency · Closed
- Broadcasting channels need have neither extremumtruth-dependency · Closed
- ChannelTimeReversalNoGotruth-dependency · Closed
- Coherent compression of a positive orbittruth-dependency · Closed
- Concealment does not determine the adjoint kerneltruth-dependency · Closed
- Effect probability extensiontruth-dependency · Closed
- Entanglement-assisted communication value and the output dimensiontruth-dependency · Closed
- Infinitely many extreme classes in matrix D-majorizationtruth-dependency · Closed
- Positive refinement rigiditytruth-dependency · Closed
- Real Copy Statistics and Conjugationtruth-dependency · Closed
- The spatiotemporal Born rule dichotomytruth-dependency · Closed
- Unitary entanglement assistance under a vacuum energy restrictiontruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A non-extreme minimum-rank superchannel extensionstructural-affinity · Closed
- A quantitative detector-rank horizonstructural-affinity · Closed
- A qutrit obstruction to CP-filter equivalence with the channel transposestructural-affinity · Closed
- Advantage-quantum measurements cannot be simulated with finitely many copiesstructural-affinity · Closed
- Broadcasting channels need have neither extremumstructural-affinity · Closed
- Coherent compression of a positive orbitstructural-affinity · Closed
- Concealment does not determine the adjoint kernelstructural-affinity · Closed
- Effect probability extensionstructural-affinity · Closed
- Entanglement-assisted communication value and the output dimensionstructural-affinity · Closed
- Flat-spectrum probe probabilitiesstructural-affinity · Closed
- Infinitely many extreme classes in matrix D-majorizationstructural-affinity · Closed
- KrausLeftInverseNecessitystructural-affinity · Closed
- Positive refinement rigiditystructural-affinity · Closed
- Real Copy Statistics and Conjugationstructural-affinity · Closed
- Static and Dynamic Projection Diagnostics Are Independentstructural-affinity · Closed
- The spatiotemporal Born rule dichotomystructural-affinity · Closed
- Unitary entanglement assistance under a vacuum energy restrictionstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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