Yanase

Yanase's inequality is a principle in quantum mechanics that relates the precision with which certain pairs of properties—called observables—can be simultaneously measured. If two variables are incompatible (like position and momentum), gaining more accuracy in measuring one typically causes less precision in measuring the other. Yanase's inequality formalizes this trade-off, defining the limits of measurement accuracy and disturbance for quantum systems. It helps scientists understand the fundamental constraints when observing quantum phenomena, emphasizing that some properties cannot both be precisely known or measured at the same time due to the intrinsic nature of quantum mechanics.