Abstract

The statistical nature of measurements alone easily causes unphysical estimates in quantum state tomography (QST). Multinomial or Poissonian noise results in eigenvalue distributions converging to the Wigner semicircle distribution for already a modest number of qubits [1], see Fig. 1a). This enables one to estimate the influence of finite statistics to QST as well as the number of measurements necessary to avoid unphysical solutions. Knowing the impact of statistical noise on the eigenvalue distribution also directly leads to a physical state estimate with minimal numerical effort. Combining ideas from random matrix theory with pertubation theory, one can even obtain confidence regions for the state as well as for figures of merit like the fidelity.

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