Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a particular subset of the data is considered. Here, we experimentally demonstrated an anomalous weak value can be obtained without discarding any data by performing a sequential weak measurement on a single-qubit system. By controlling the blazing density of the hologram on a spatial light modulator, the measurement strength can be conveniently controlled. Such an anomalous phenomenon disappears when the measurement strength becomes strong. Moreover, we find that the anomalous weak value can not be observed without post-selection when the sequential measurement is performed on each of the components of a two-qubit system, which confirms that the observed anomalous weak value is based on sequential weak measurement of two noncommutative operators.

中文翻译：

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无后选异常弱值的实验观察

弱测量已被证明在研究基本问题和实际问题中都发挥着重要作用。通常认为只有在执行后选择时才会观察到异常弱值，即仅考虑数据的特定子集。在这里，我们通过实验证明，通过在单量子位系统上执行顺序弱测量，可以在不丢弃任何数据的情况下获得异常弱值。通过控制空间光调制器上全息图的闪耀密度，可以方便地控制测量强度。当测量强度变强时，这种异常现象就会消失。此外，我们发现当对双量子位系统的每个组件进行顺序测量时，如果没有后选择，则无法观察到异常弱值，