QuantumChannels / CONCEPT
Relative quantumness can increase under a commutativity-preserving channel
A completely positive, trace-preserving qubit channel that preserves commuting density matrices increases relative quantumness at alpha zero. The exact trace arguments of the logarithms are 50401283/7340144 before the channel and 1879639/266240 afterwards.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES15
PROOF DEPTH2
DOCUMENT LINKS1
A qubit refutation
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A negative damped spin distribution satisfying the Husimi coefficient boundtruth-dependency · Closed
- A qutrit obstruction to CP-filter equivalence with the channel transposetruth-dependency · Closed
- A stochastic qutrit channel that is not unitaltruth-dependency · Closed
- Data processing fails for the cumulant-based Renyi functional at every order above onetruth-dependency · Closed
- Divisibility does not force entanglement breaking for qutritstruth-dependency · Closed
- FaithfulPerronRegularizationtruth-dependency · Closed
- FormationBoundstruth-dependency · Closed
- Purify-and-clone is not optimal for one-site worst-case risktruth-dependency · Closed
- QubitWassersteinCouplingstruth-dependency · Closed
- Semi-nonnegative maps can exhibit information backflowtruth-dependency · Closed
- Tensor rules for the qubit Wigner distancetruth-dependency · Closed
- The minimum overlap of orthogonal channel inputstruth-dependency · Closed
- Three-weight Pauli channels have Bayesian inverses only at the maximally mixed statetruth-dependency · Closed
- Unital-block overlap can be less than minus onetruth-dependency · Closed
- WassersteinComplexityNonconvextruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A degree-three counterexample to the higher-order C*-algebraic Smale conjecturestructural-affinity · Closed
- A negative damped spin distribution satisfying the Husimi coefficient boundstructural-affinity · Closed
- A qutrit obstruction to CP-filter equivalence with the channel transposestructural-affinity · Closed
- A stochastic qutrit channel that is not unitalstructural-affinity · Closed
- Data processing fails for the cumulant-based Renyi functional at every order above onestructural-affinity · Closed
- Diagonal Kraus Instrument Factorizationstructural-affinity · Closed
- Divisibility does not force entanglement breaking for qutritsstructural-affinity · Closed
- FaithfulPerronRegularizationstructural-affinity · Closed
- Finite Kraus Quantum Channelsstructural-affinity · Closed
- Flat-spectrum probe probabilitiesstructural-affinity · Closed
- KrausLeftInverseNecessitystructural-affinity · Closed
- Nearest point in the four-coordinate edge polytopestructural-affinity · Closed
- RetainedLocalProtocolstructural-affinity · Closed
- Semi-nonnegative maps can exhibit information backflowstructural-affinity · Closed
- Tensor rules for the qubit Wigner distancestructural-affinity · Closed
- The Choi spectrum of unital product-unitary-equivariant mapsstructural-affinity · Closed
- The minimum overlap of orthogonal channel inputsstructural-affinity · Closed
- Three-weight Pauli channels have Bayesian inverses only at the maximally mixed statestructural-affinity · Closed
- Unital-block overlap can be less than minus onestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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