Quantum / CONCEPT
Finite Kraus Representations
Every finite rectangular completely positive matrix map has a finite Kraus witness.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES18
PROOF DEPTH2
DOCUMENT LINKS0
Complete positivity gives a rectangular Kraus family
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A counterexample to Fan–Wu–Fei channel coherence dominationtruth-dependency · Closed
- A non-extreme minimum-rank superchannel extensiontruth-dependency · Closed
- A quantitative detector-rank horizontruth-dependency · Closed
- ActualChannelAlgebratruth-dependency · Closed
- Compatibility need not imply Jordan compatibilitytruth-dependency · Closed
- Conditional min-entropy of noisy unitariestruth-dependency · Closed
- Entanglement-assisted communication value and the output dimensiontruth-dependency · Closed
- Equivalence of PPT-squared and IPT-squaredtruth-dependency · Closed
- Heisenberg Channel Compression Equivalencetruth-dependency · Closed
- Passive memory with a nonclassical Gram matrixtruth-dependency · Closed
- Pauli-weight expansion and alternating truncation bounds for qubit SIC k-fidelitiestruth-dependency · Closed
- ProbeComponentRigiditytruth-dependency · Closed
- Rank-One Feedback and the First Readtruth-dependency · Closed
- Real Readouts and Complete Positivitytruth-dependency · Closed
- The qutrit complementary-entropy frontiertruth-dependency · Closed
- Three-weight Pauli channels have Bayesian inverses only at the maximally mixed statetruth-dependency · Closed
- Uniqueness of the upper-boundary deferred-measurement instrumenttruth-dependency · Closed
- Weighted defects of finite operator wordstruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A counterexample to Fan–Wu–Fei channel coherence dominationstructural-affinity · Closed
- A negative damped spin distribution satisfying the Husimi coefficient boundstructural-affinity · Closed
- A non-extreme minimum-rank superchannel extensionstructural-affinity · Closed
- A quantitative detector-rank horizonstructural-affinity · Closed
- A qubit pure-program obstructionstructural-affinity · Closed
- Achievable (k-fidelity, process fidelity) regions and single-fidelity non-identifiabilitystructural-affinity · Closed
- ActualChannelAlgebrastructural-affinity · Closed
- Compatibility need not imply Jordan compatibilitystructural-affinity · Closed
- Complex sparse-probe coercivitystructural-affinity · Closed
- Conditional min-entropy of noisy unitariesstructural-affinity · Closed
- Cyclic Refractory Quantum Generatorstructural-affinity · Closed
- Diagonal Kraus Instrument Factorizationstructural-affinity · Closed
- Entanglement-assisted communication value and the output dimensionstructural-affinity · Closed
- Equivalence of PPT-squared and IPT-squaredstructural-affinity · Closed
- Finite causal schedules as executable quantum relation graphsstructural-affinity · Closed
- Finite instruments as a fixed quantum relation graphstructural-affinity · Closed
- Finite Kraus Quantum Channelsstructural-affinity · Closed
- Finite Shifted Record Realizationstructural-affinity · Closed
- FiniteLocalProtocolstructural-affinity · Closed
- FinitePreparationChannelstructural-affinity · Closed
- Flat-spectrum probe probabilitiesstructural-affinity · Closed
- Heisenberg Channel Compression Equivalencestructural-affinity · Closed
- Passive memory with a nonclassical Gram matrixstructural-affinity · Closed
- Pauli-weight expansion and alternating truncation bounds for qubit SIC k-fidelitiesstructural-affinity · Closed
- Positive refinement of a coarse qubit mapstructural-affinity · Closed
- ProbeComponentRigiditystructural-affinity · Closed
- Pure targets prevent general square-root savingsstructural-affinity · Closed
- Quantitative word orthonormal extensionstructural-affinity · Closed
- Rank-One Feedback and the First Readstructural-affinity · Closed
- Real Readouts and Complete Positivitystructural-affinity · Closed
- RetainedLocalProtocolstructural-affinity · Closed
- The Choi spectrum of unital product-unitary-equivariant mapsstructural-affinity · Closed
- The gcd-three equator formula fails at dimension sixstructural-affinity · Closed
- The least trace-distance contraction coefficient over a classical channelstructural-affinity · Closed
- The qutrit complementary-entropy frontierstructural-affinity · Closed
- Three-weight Pauli channels have Bayesian inverses only at the maximally mixed statestructural-affinity · Closed
- Trace-preserving linear reconstruction and CPTP joint k-fidelity simplex geometrystructural-affinity · Closed
- Uniqueness of the upper-boundary deferred-measurement instrumentstructural-affinity · Closed
- Weighted defects of finite operator wordsstructural-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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