{
  "id": "1702.07921",
  "version": "v1",
  "published": "2017-02-25T16:58:14.000Z",
  "updated": "2017-02-25T16:58:14.000Z",
  "title": "Quantum Wasserstein-1 Distance",
  "authors": [
    "Yongxin Chen",
    "Tryphon T. Georgiou",
    "Lipeng Ning",
    "Allen Tannenbaum"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular, a \"dual of the dual\" formulation of $W_1$. This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-25T16:58:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "earth movers distance",
      "matrix probability densities",
      "matrix analogue",
      "matrix-valued density measures",
      "duality theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}