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.

中文翻译：

---

通过顺序使用相同的信息不完整的测量设备的量子态层析成像

摘要

一个的状态\（d \）维量子系统只能由具有执行信息上完整的测量中推断出\（米\ geqslant d ^ {2} \）的结果。但是，实验上可获得的测量结果可能在信息上不完整。在这里，我们表明，如果连续应用几次，单个信息不完整的测量设备仍然能够提供有关量子系统的所有信息。我们推导了这种测量设备的必要和充分条件，并给出了量子位，量子态，一般\（d \）级系统和\（n \）复合系统的示例。量子位，在这种测量设备存在的地方。我们表明，在考虑的情况下，投影测量和具有2个结果的Lüders测量是无用的。