Quantum / CONCEPT
Purify-and-clone is not optimal for one-site worst-case risk
A symmetric quantum channel has one-site worst-case infidelity at most one sixth, while purify-and-clone has risk at least one fifth in system and environment dimension two.
Closed
DIRECT PREREQUISITES15
DIRECT CONSEQUENCES2
PROOF DEPTH22
DOCUMENT LINKS0
vecPure_rank_one
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
- Broadcasting channels need have neither extremumtruth-dependency · Closed
- Determinant-integral subentropytruth-dependency · Closed
- Finite Density States and Quantum Channelstruth-dependency · Closed
- Finite Kraus Quantum Channelstruth-dependency · Closed
- Finite sign twirls and entropy gapstruth-dependency · Closed
- Finite-Dimensional Quantum Skeletonstruth-dependency · Closed
- Partial Trace and Quantum Mutual Informationtruth-dependency · Closed
- Passive memory with a nonclassical Gram matrixtruth-dependency · Closed
- Projected Unitary Dynamicstruth-dependency · Closed
- QubitWassersteinCouplingstruth-dependency · Closed
- Relative quantumness can increase under a commutativity-preserving channeltruth-dependency · Closed
- Robustness of ancilla-free testerstruth-dependency · Closed
- The Pure-State Handshaketruth-dependency · Closed
- The two-copy Haar moment and its local ruletruth-dependency · Closed
- WassersteinComplexityNonconvextruth-dependency · Closed
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A symmetric injective matrix-product family with four physical levelsstructural-affinity · Closed
- Broadcasting channels need have neither extremumstructural-affinity · Closed
- Even-depth permuted brickwork fails positive semidefinitenessstructural-affinity · Closed
- Finite Memory History Capacitystructural-affinity · Closed
- Finite sign twirls and entropy gapsstructural-affinity · Closed
- Genuine entanglement and commutation rankstructural-affinity · Closed
- Passive memory with a nonclassical Gram matrixstructural-affinity · Closed
- Pauli Fisher information along a GHZ phase familystructural-affinity · Closed
- QubitWassersteinCouplingsstructural-affinity · Closed
- Robustness of ancilla-free testersstructural-affinity · Closed
- Square-Free Source Jets as Cyclic Tracesstructural-affinity · Closed
- The sharp fidelity bound for marginal process approximationsstructural-affinity · Closed
- The two-copy Haar moment and its local rulestructural-affinity · Closed
- WassersteinComplexityNonconvexstructural-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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