{
  "id": "2312.16583",
  "version": "v1",
  "published": "2023-12-27T14:19:22.000Z",
  "updated": "2023-12-27T14:19:22.000Z",
  "title": "Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots",
  "authors": [
    "Igor Bragar",
    "Łukasz Cywiński"
  ],
  "comment": "13 pages + appendices",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_{0}$) qubits operated in a regime when energy associated with the magnetic field gradient, $\\Delta B_{z}$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $\\Delta B_{z}$ and quasistatical or dynamical $1/f^{\\beta}$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^{\\beta}$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by uncorrelated $1/f^{\\beta}$ charge noises.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-27T14:19:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaas quantum dots",
      "maximal level",
      "singlet-triplet qubits",
      "entanglement",
      "limitations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}