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@ARTICLE{Amaro:888651,
      author       = {Amaro, David and Müller, Markus and Pal, Amit Kumar},
      title        = {{S}calable characterization of localizable entanglement in
                      noisy topological quantum codes},
      journal      = {New journal of physics},
      volume       = {22},
      number       = {5},
      issn         = {1367-2630},
      address      = {[London]},
      publisher    = {IOP},
      reportid     = {FZJ-2020-05094},
      pages        = {053038 -},
      year         = {2020},
      abstract     = {Topological quantum error correcting codes have emerged as
                      leading candidates towards the goal of achieving large-scale
                      fault-tolerant quantum computers. However, quantifying
                      entanglement in these systems of large size in the presence
                      of noise is a challenging task. In this paper, we provide
                      two different prescriptions to characterize noisy stabilizer
                      states, including the surface and the color codes, in terms
                      of localizable entanglement over a subset of qubits. In one
                      approach, we exploit appropriately constructed entanglement
                      witness operators to estimate a witness-based lower bound of
                      localizable entanglement, which is directly accessible in
                      experiments. In the other recipe, we use graph states that
                      are local unitary equivalent to the stabilizer state to
                      determine a computable measurement-based lower bound of
                      localizable entanglement. If used experimentally, this
                      translates to a lower bound of localizable entanglement
                      obtained from single-qubit measurements in specific bases to
                      be performed on the qubits outside the subsystem of
                      interest. Towards computing these lower bounds, we discuss
                      in detail the methodology of obtaining a local unitary
                      equivalent graph state from a stabilizer state, which
                      includes a new and scalable geometric recipe as well as an
                      algebraic method that applies to general stabilizer states
                      of arbitrary size. Moreover, as a crucial step of the latter
                      recipe, we develop a scalable graph-transformation algorithm
                      that creates a link between two specific nodes in a graph
                      using a sequence of local complementation operations. We
                      develop open-source Python packages for these
                      transformations, and illustrate the methodology by applying
                      it to a noisy topological color code, and study how the
                      witness and measurement-based lower bounds of localizable
                      entanglement varies with the distance between the chosen
                      qubits.},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000538446700001},
      doi          = {10.1088/1367-2630/ab84b3},
      url          = {https://juser.fz-juelich.de/record/888651},
}