Quantum / CONCEPT
The negativity of randomized graph states is not monotone
Wu, Rossi, Kampermann, Severini, Kwek, Macchiavello and Bruss (arXiv:1403.3828, Section V) ask whether the negativity of a randomized graph state, across any bipartition, increases monotonically with the probability p that each edge is present. It does not: for the complete bipartite graph K_(3,3) and the bipartition into its two parts, the negativity is larger than 1/2 at p = 97/100 and at most 1/2 at p = 1.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES5
PROOF DEPTH5
DOCUMENT LINKS1
The answer is negative
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A genuine four-state superposition from level-one QAOAtruth-dependency · Closed
- Lidar Restricted Anticoncentration Refutationtruth-dependency · Closed
- Preparation error need not increase purification output errortruth-dependency · Closed
- Subsystem size does not order coherent informationtruth-dependency · Closed
- The worst-case CNOT lower bound for reflection symmetrytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A genuine four-state superposition from level-one QAOAstructural-affinity · Closed
- Counting even labels in a CNOT sequencestructural-affinity · Closed
- Finite Trace Distancestructural-affinity · Closed
- Lidar Restricted Anticoncentration Refutationstructural-affinity · Closed
- Preparation error need not increase purification output errorstructural-affinity · Closed
- Subsystem size does not order coherent informationstructural-affinity · Closed
- The exact three-coherence Ramsey thresholdstructural-affinity · Closed
- The five-cycle graph state is strongly 1-resistantstructural-affinity · Closed
- The six-cycle graph state is not strongly 2-resistantstructural-affinity · Closed
- The worst-case CNOT lower bound for reflection symmetrystructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
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LIBRARY / RELEASE VERSIONS
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