New fundamental limitation restricts position accuracy of quantum objects: In the new study, Busch and Loveridge have analyzed Ozawa’s model and found that, contrary to Ozawa’s conclusion, momentum conservation does in fact limit the accuracy and repeatability of position measurements: they have shown that good accuracy and repeatability of a position measurement can only be achieved by using a sufficiently large apparatus.
The researchers also developed an alternative model that identifies a particular condition underlying the WAY theorem: the so-called Yanase condition, which stipulates the compatibility of the indicator variable of the apparatus with the conserved quantity. This alternative model shows that, if it were allowed to disregard and violate the Yanase condition, position measurements could be done with arbitrary accuracy, even with a small apparatus. However, if one tries to exploit this escape route from the WAY theorem, one is only faced by the puzzling prospect of the same limitation reappearing for the apparatus indicator variable.
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