Abstract
State of a \(d\)-dimensional quantum system can only be inferred by performing an informationally complete measurement with \(m\geqslant d^{2}\) outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied several times in a row. We derive a necessary and sufficient condition for such a measuring apparatus and give illustrative examples for qubits, qutrits, general \(d\)-level systems, and composite systems of \(n\) qubits, where such a measuring apparatus exists. We show that projective measurements and Lüders measurements with 2 outcomes are useless in the considered scenario.
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Zhuravlev, V.A., Filippov, S.N. Quantum State Tomography Via Sequential Uses of the Same Informationally Incomplete Measuring Apparatus. Lobachevskii J Math 41, 2405–2414 (2020). https://doi.org/10.1134/S1995080220120434
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DOI: https://doi.org/10.1134/S1995080220120434