QuantumChannels / CONCEPT
Data processing fails for the cumulant-based Renyi functional at every order above one
Meunson and Deesuwan (arXiv:2606.31205) define a cumulant-based quantum relative Renyi functional for alpha > 1 and state in the abstract and conclusion that its quantum data-processing inequality under arbitrary CPTP maps remains open. For every alpha > 1 a pair of positive definite qubit states and the complete dephasing channel increase the functional, so the inequality fails at every order above one.
Closed
DIRECT PREREQUISITES4
DIRECT CONSEQUENCES3
PROOF DEPTH6
DOCUMENT LINKS0
Functional calculus for a self-adjoint involution
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
- Entropy Production by Coherence Deletiontruth-dependency · Closed
- Relative quantumness can increase under a commutativity-preserving channeltruth-dependency · Closed
- Static and Dynamic Projection Diagnostics Are Independenttruth-dependency · Closed
- Two-point functional calculustruth-dependency · Closed
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A qutrit obstruction to CP-filter equivalence with the channel transposestructural-affinity · Closed
- Concealment does not determine the adjoint kernelstructural-affinity · Closed
- Entropy Production by Coherence Deletionstructural-affinity · Closed
- Off-midpoint obstruction for the original spectral meanstructural-affinity · Closed
- Quantum Channels: Pinching Projectionstructural-affinity · Closed
- Relative quantumness can increase under a commutativity-preserving channelstructural-affinity · Closed
- Scalar dependencies of the UNTILDE proofstructural-affinity · Closed
- Standard-Basis Qubit Pinchingstructural-affinity · Closed
- Static and Dynamic Projection Diagnostics Are Independentstructural-affinity · Closed
- Subadditivity of quantum states over timestructural-affinity · Closed
- Subsystem size does not order coherent informationstructural-affinity · Closed
- The proposed noncommuting Tsallis bound order failsstructural-affinity · Closed
- Two-point functional calculusstructural-affinity · Closed
Documents & exposition
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Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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