In our latest interferometric experiment 1 we compare measurements of the Ozawa-Hall error and the measured lower bound of Ozawa’s universally valid uncertainty relations as function of initial states’s phase for observables and . The former is a which-way observable in an interferometer, while the latter observable is associated with the output of the interferometer. Since the first observable is measured in a non-invasive manner, applying the so-called feedback compensation (see 2 for details), the measurement of the second observable is not disturbed. This results in a tight version of Ozawa’s universally valid uncertainty relation, denoted as , where we experimentally verify both sides of the (in)equality, applying the setup depicted below.
The measurement error vanishes completely for phase settings where the weak value is purely real (imaginary part is zero). Since the lower bound of the uncertainty relation is given by the gradient of the interference fringe the bound also vanishes at the same phases, namely and . This illustrates that in Ozawa’s theory of measurement errors the imaginary part of the weak value is associated with the error (see here for details of the experiment and more results). This work was supported by the Austrian science fund (FWF) Projects No. P 34239, P 30677, and P 34105.
1. Andreas Dvorak, Ismaele V. Masiello, Yuji Hasegawa, Hartmut Lemmel, Holger F. Hofmann, and Stephan Sponar, Phys. Rev. Res. 7, 043334 (2025). ↩
2. Hartmut Lemmel, Niels Geerits, Armin Danner, Holger F. Hofmann, and Stephan Sponar, Phs. Rev. Research 4, 023075 (2022). ↩