{
  "title": "Noncommutative Information Measurement Aqec Dependency Map",
  "question": "Which map, state-domain, equality, localization, and algebra hypotheses lead from a von Neumann channel to recovery, measurement, and algebraic-QEC conclusions?",
  "takeaway": "Normal complete positivity licenses state transport and data processing; exact recovery additionally needs equality and reference support, while localized measurement follows a separate compact-coupling and causal-factorization branch.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "local von Neumann algebras\\\\normal states and supports"
    },
    {
      "id": "n1",
      "label": "normal UCP channel $\\Phi$\\\\normal CP instrument branches"
    },
    {
      "id": "n2",
      "label": "relative modular data\\\\Araki data processing"
    },
    {
      "id": "n3",
      "label": "equality for a declared family\\\\faithful reference or support reduction"
    },
    {
      "id": "n4",
      "label": "Petz map or expectation\\\\correctable algebra $\\mathfrak A$"
    },
    {
      "id": "n5",
      "label": "scoped applications\\\\split, finite index, or type III"
    },
    {
      "id": "branch",
      "label": "compact coupling $K$ gives $\\Theta$\\\\causal factorization orders instruments"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "map",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "DPI",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "equality",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "recover",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "scope",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "branch",
      "label": "measurement path",
      "logical_status": "licensed implication"
    }
  ]
}