{
  "annotation_id": "9af8c0ce-3799-4296-bb08-c5e75e127ac4",
  "date_created": "2026-03-02T18:02:13.452000Z",
  "date_modified": "2026-03-02T18:02:13.452000Z",
  "file_hash": "fa71df7bedc17f5f62558b4b33505e075d01654ed3d2442e8ca30e521c024b9c",
  "private": false,
  "record": {
    "abstract": "Mathematical foundation of the novel concept of quantum tensor product by\nZanardi et al is rigorously established. The concept of relative quantum\nentanglement is naturally introduced and its meaning is made clear both\nmathematically and physically. For a finite or an infinite dimensional vector\nspace $W$ the so called tensor product partition (TPP) is introduced on\n$End(W)$, the set of endmorphisms of $W$, and a natural correspondence is\nconstructed between the set of TPP\u0027s of $End(W)$ and the set of tensor product\nstructures (TPS\u0027s) of $W$. As a byproduct, it is shown that an arbitrarily\ngiven wave function belonging to an n-dimensional Hilbert space, $n$ being not\na prime number, can be interpreted as a separable state with respect to some\nman-made TPS, and thus a quantum entangled state of a many-body system with\nrespect to the \"God-given\" TPS can be regarded as a quantum state without\nentanglement in some sense. The concept of standard set of observables is also\nintroduced to probe the underlying structure of the object TPP and to establish\nits connection with practical physical measurement.",
    "arxiv_id": "quant-ph/0410245",
    "authors": [
      "X. F. Liu",
      "C. P. Sun"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the relative quantum entanglement with respect to tensor product   structure",
    "url": "https://arxiv.org/abs/quant-ph/0410245"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a0307624-2012-49b7-a3df-6886293f98b1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}