{
  "annotation_id": "28883a22-1316-4c10-8fe8-74f998d28d86",
  "date_created": "2026-03-02T18:02:23.672000Z",
  "date_modified": "2026-03-02T18:02:23.672000Z",
  "file_hash": "40e0e7efb82516d3c8443fc8b205ad2002ae54c8278b589d72c4223b051a76fd",
  "private": false,
  "record": {
    "abstract": "Suppose we have an n-qubit system, and we are given a collection of local\ndensity matrices rho_1,...,rho_m, where each rho_i describes some subset of the\nqubits. We say that rho_1,...,rho_m are \"consistent\" if there exists a global\nstate sigma (on all n qubits) whose reduced density matrices match\nrho_1,...,rho_m.\n  We prove the following result: if rho_1,...,rho_m are consistent with some\nstate sigma \u003e 0, then they are also consistent with a state sigma\u0027 of the form\nsigma\u0027 = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on\nthe same qubits as rho_i, and Z is a normalizing factor. (This is known as a\nGibbs state.) Actually, we show a more general result, on the consistency of a\nset of expectation values \u003cT_1\u003e,...,\u003cT_r\u003e, where the observables T_1,...,T_r\nneed not commute. This result was previously proved by Jaynes (1957) in the\ncontext of the maximum-entropy principle; here we provide a somewhat different\nproof, using properties of the partition function.",
    "arxiv_id": "quant-ph/0603012",
    "authors": [
      "Yi-Kai Liu"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Gibbs States and the Consistency of Local Density Matrices",
    "url": "https://arxiv.org/abs/quant-ph/0603012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "92f92d84-3723-4676-b9bd-4a41ebf64f07",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}