Quantum / CONCEPT
Finite Trace Distance
Trace norm, actual density-state distance, and contraction for every canonical quantum channel.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES29
PROOF DEPTH1
DOCUMENT LINKS0
The Gram matrix computes transformed inner products
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A counterexample to the maximal reverse Pinsker boundtruth-dependency · Closed
- A generic-state counterexample in the kicked Ising chaintruth-dependency · Closed
- Bound coherence in every dimension at least threetruth-dependency · Closed
- Branch-Conditioned Trace Distancetruth-dependency · Closed
- Centered Kraus trace norm on finite referencestruth-dependency · Closed
- Comparability of conical-design concurrence boundstruth-dependency · Closed
- Expanding square matrices and their singular valuestruth-dependency · Closed
- Finite Record Recovery Errortruth-dependency · Closed
- Finite Reference Channel Distancetruth-dependency · Closed
- Finite Sector Channel Optimalitytruth-dependency · Closed
- Negativity is not the partial transpose distance to the PPT statestruth-dependency · Closed
- Optimality of the coefficient in the entanglement-breaking norm inequalitytruth-dependency · Closed
- Rare-Branch Conditional Error Sharpnesstruth-dependency · Closed
- Real rectangular nuclear-norm additivitytruth-dependency · Closed
- Schur Channel Upper Boundtruth-dependency · Closed
- Selective LOCC can increase the Moreau-Yosida entanglement of formationtruth-dependency · Closed
- The Alsing–Birrittella logarithmic-negativity sandwichtruth-dependency · Closed
- The least trace-distance contraction coefficient over a classical channeltruth-dependency · Closed
- The lower Gelfand–Naimark ratio inequalitytruth-dependency · Closed
- The negativity of randomized graph states is not monotonetruth-dependency · Closed
- The overlap-to-purity part of Kopel's equality theoremtruth-dependency · Closed
- The qutrit overlap entropy bound is unattainabletruth-dependency · Closed
- The three-state root-fidelity Holevo boundtruth-dependency · Closed
- The trace-corrected arithmetic boundtruth-dependency · Closed
- Trace-norm CMI contraction conjecturetruth-dependency · Closed
- Two unbounded entanglement gaps with one qubittruth-dependency · Closed
- Unitarily invariant norms and symmetric diagonal gaugestruth-dependency · Closed
- Weighted Bottcher-Wenzel, case (ii)truth-dependency · Closed
- Werner states undetected by all complex testerstruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A counterexample to the maximal reverse Pinsker boundstructural-affinity · Closed
- Actual Adaptive Low-Instrument Effectsstructural-affinity · Closed
- Bound coherence in every dimension at least threestructural-affinity · Closed
- Bounded Adaptive Low-Instrument Effectsstructural-affinity · Closed
- Branch-Conditioned Trace Distancestructural-affinity · Closed
- Centered Kraus trace norm on finite referencesstructural-affinity · Closed
- Comparability of conical-design concurrence boundsstructural-affinity · Closed
- Complete retained golden historiesstructural-affinity · Closed
- Expanding square matrices and their singular valuesstructural-affinity · Closed
- Finite Density States and Quantum Channelsstructural-affinity · Closed
- Finite Record Recovery Errorstructural-affinity · Closed
- Finite Reference Channel Distancestructural-affinity · Closed
- Independent Source Noise in a Quantum Trianglestructural-affinity · Closed
- Negativity is not the partial transpose distance to the PPT statesstructural-affinity · Closed
- Optimality of the coefficient in the entanglement-breaking norm inequalitystructural-affinity · Closed
- Physical EJM Noise Boundsstructural-affinity · Closed
- Rare-Branch Conditional Error Sharpnessstructural-affinity · Closed
- Real rectangular nuclear-norm additivitystructural-affinity · Closed
- Schur Channel Upper Boundstructural-affinity · Closed
- Sector Schmidt Encodingsstructural-affinity · Closed
- Support-Aware Quantum Relative Entropystructural-affinity · Closed
- The Alsing–Birrittella logarithmic-negativity sandwichstructural-affinity · Closed
- The geometric core of nuclear-norm additivitystructural-affinity · Closed
- The least trace-distance contraction coefficient over a classical channelstructural-affinity · Closed
- The lower Gelfand–Naimark ratio inequalitystructural-affinity · Closed
- The negativity of randomized graph states is not monotonestructural-affinity · Closed
- The overlap-to-purity part of Kopel's equality theoremstructural-affinity · Closed
- The qutrit overlap entropy bound is unattainablestructural-affinity · Closed
- The Thue-Morse prefix 01101001 needs more than one qubitstructural-affinity · Closed
- Trace-norm CMI contraction conjecturestructural-affinity · Closed
- Uniform variance and block centeringstructural-affinity · Closed
- Unitarily invariant norms and symmetric diagonal gaugesstructural-affinity · Closed
- Weighted Bottcher-Wenzel, case (ii)structural-affinity · Closed
- Werner states undetected by all complex testersstructural-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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