{
  "annotation_id": "326f4e59-4fe2-4e37-b279-1c067117989e",
  "date_created": "2026-03-02T18:02:06.646000Z",
  "date_modified": "2026-03-02T18:02:06.646000Z",
  "file_hash": "cd31bc53e4b12ca3d91fa952461194f40ed1005d4ed325990bf903402d5d83d7",
  "private": false,
  "record": {
    "abstract": "We study the convex set of all bipartite quantum states with fixed marginal\nstates. The extremal states in this set have recently been characterized by\nParthasarathy [Ann. Henri Poincar\\\u0027e (to appear), quant-ph/0307182, [1]]. Here\nwe present an alternative necessary and sufficient condition for a state with\ngiven marginals to be extremal. Our approach is based on a canonical duality\nbetween bipartite states and a certain class of completely positive maps and\nhas the advantage that it is easier to check and to construct explicit examples\nof extremal states. In dimension 2 x 2 we give a simple new proof for the fact\nthat all extremal states with maximally mixed marginals are precisely the\nprojectors onto maximally entangled wave functions. We also prove that in\nhigher dimension this does not hold and construct an explicit example of an\nextremal state with maximally mixed marginals in dimension 3 x 3 that is not\nmaximally entangled. Generalizations of this result to higher dimensions are\nalso discussed.",
    "arxiv_id": "quant-ph/0406021",
    "authors": [
      "Oliver Rudolph"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1776642",
    "journal_ref": "J.Math.Phys. 45 (2004), 4035-4041",
    "title": "On extremal quantum states of composite systems with fixed marginals",
    "url": "https://arxiv.org/abs/quant-ph/0406021"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fb7bef54-5e03-4e2c-bd86-ff5659fcad78",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}