{
  "annotation_id": "f999ea15-4823-47d5-b23a-a5bad7643ae6",
  "date_created": "2026-03-02T18:02:27.285000Z",
  "date_modified": "2026-03-02T18:02:27.285000Z",
  "file_hash": "c570c895612f9abd5b6b72985cc90a70356db9f948cec652260157151b3cc521",
  "private": false,
  "record": {
    "abstract": "Let M be the set of mixed states and S the set of separable states of the\ntwo-qubit system, and G = SU(2) x SU(2) the group of local unitary\ntransformations (ignoring the overall phase factor). We compute the multigraded\nPoincare series for the algebra of G-invariant polynomial functions on the\naffine space of all Hermitian operators of trace 1. We check that this series\nis consistent with the list of invariants computed by Makhlin. By using the\nrecent result of Augusiak et al., we show that the boundary of S decomposes\nnaturally into two pieces. We prove that the part of this boundary which is\ncontained in the relative interior of M is a smooth manifold.",
    "arxiv_id": "quant-ph/0604190",
    "authors": [
      "Dragomir Z. Djokovic"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Multigraded Poincare series for mixed states of two qubits and the   boundary of the set of separable states",
    "url": "https://arxiv.org/abs/quant-ph/0604190"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b017914b-a3bc-4cbc-9cb6-4d7033531def",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}