{
  "id": "1305.3672",
  "version": "v1",
  "published": "2013-05-16T02:41:29.000Z",
  "updated": "2013-05-16T02:41:29.000Z",
  "title": "Restriction on the rank of marginals of bipartite pure states",
  "authors": [
    "S. V. M. Satyanarayana"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "Consider a qubit-qutrit ($2 \\times 3$) composite state space. Let $C(\\{1}{2}I_2, \\{1}{3}I_3)$ be a convex set of all possible states of composite system whose marginals are given by $\\{1}{2}I_2$ and $\\{1}{3}I_3$ in two and three dimensional spaces respectively. We prove that there exists no pure state in $C(\\{1}{2}I_2, \\{1}{3}I_3)$. Further we generalize this result to an arbitrary $m \\times n$ bipartite systems. We prove that for $m < n$, no pure state exists in the convex set $C(\\rho_A,\\rho_B)$, for an arbitrary $\\rho_A$ and rank of $\\rho_B >m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-16T02:41:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite pure states",
      "convex set",
      "restriction",
      "composite state space",
      "composite system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.3672S"
    }
  }
}