@article{Ivanova2021Quant-52409.2,
  year={2021},
  doi={10.1088/1367-2630/ac3c0e},
  title={Quantum state tomography as a numerical optimization problem},
  volume={23},
  journal={New Journal of Physics},
  author={Ivanova, Violeta and Burkard, Guido and Rohling, Niklas},
  note={Article Number: 123034}
}

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    <dcterms:abstract xml:lang="eng">We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups including measurements restricted to a subsystem. To illustrate the power of this method we present results for the six-dimensional Hilbert space constituted by a qubit-qutrit system, which could be realized e.g. by the N-14 nuclear spin-1 and two electronic spin states of a nitrogen-vacancy center in diamond. Measurements of the qubit subsystem are expressed by projectors of rank three, i.e., projectors on half-dimensional subspaces. For systems consisting only of qubits, it was shown analytically that a set of projectors on half-dimensional subspaces can be arranged in an informationally optimal fashion for quantum state tomography, thus forming so-called mutually unbiased subspaces. Our method goes beyond qubits-only systems and we find that in dimension six such a set of mutually-unbiased subspaces can be approximated with a deviation irrelevant for practical applications.</dcterms:abstract>
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