{
  "annotation_id": "38b1fd52-d919-4e93-85f1-e4a867000b27",
  "date_created": "2026-03-02T18:01:42.191000Z",
  "date_modified": "2026-03-02T18:01:42.191000Z",
  "file_hash": "8685d1baa9d613f61de06177973b331eac0e5e96a6b97b8cc1d8647c970093d5",
  "private": false,
  "record": {
    "abstract": "We study the polynomial functions on tensor states in $(C^n)^{\\otimes k}$\nwhich are invariant under $SU(n)^k$. We describe the space of invariant\npolynomials in terms of symmetric group representations. For $k$ even, the\nsmallest degree for invariant polynomials is $n$ and in degree $n$ we find a\nnatural generalization of the determinant. For $n,d$ fixed, we describe the\nasymptotic behavior of the dimension of the space of invariants as\n$k\\to\\infty$. We study in detail the space of homogeneous degree 4 invariant\npolynomial functions on $(C^2)^{\\otimes k}$.",
    "arxiv_id": "quant-ph/0010101",
    "authors": [
      "Jean-Luc Brylinski",
      "Ranee Brylinski"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Invariant Polynomial Functions on k qudits",
    "url": "https://arxiv.org/abs/quant-ph/0010101"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c727f6b3-4b06-4103-808e-d038ac4524b7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}