"New Uncertainty Relations in view of Weak Values"


Jaeha Lee (KEK)


We present a novel inequality of uncertainty relations valid under the circumstances where we measure only one observable, not two as conventionally conceived, but approximate the other through an appropriate choice of proxy functions. Instead of approximating the observable, we may estimate a physical parameter pertinent to the observable, allowing for the consideration of the time-energy relation as well. This 'one-measurement scheme' admits a probabilistic description in which Aharonov's weak value plays a crucial role such as the determination of the optimal proxy function that attains the lower bound of the inequality. In parameter estimation, our inequality turns into the genuine Cramér-Rao inequality with a uniquely defined classical Fisher information.

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