{
  "id": "2212.02446",
  "version": "v1",
  "published": "2022-12-05T17:42:47.000Z",
  "updated": "2022-12-05T17:42:47.000Z",
  "title": "Construction of multipartite unextendible product bases and geometric measure of entanglement of positive-partial-transpose entangled states",
  "authors": [
    "Yize Sun",
    "Baoshan Wang",
    "Shiru Li"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space $\\mathbb{C}^2\\otimes\\mathbb{C}^2\\otimes\\mathbb{C}^2\\otimes\\mathbb{C}^2\\otimes\\mathbb{C}^2\\otimes\\mathbb{C}^4$ by merging two different systems of an existing $7$-qubit UPB of size $11$. Moreover, a new family of $7$-qubit positive-partial-transpose (PPT) entangled states of rank $2^7-11$ is constructed. We analytically derive a geometric measure of entanglement of a special PPT entangled states. Also an upper bound are given by two methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T17:42:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive-partial-transpose entangled states",
      "geometric measure",
      "entanglement",
      "construction",
      "construct multipartite unextendible product bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}