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The Heisenberg uncertainty principle states that the product of the noise ina position measurement and the momentum disturbance caused by that measurementshould be no less than the limit set by Planck's constant, hbar/2, asdemonstrated by Heisenberg's thought experiment using a gamma-ray microscope.Here I show that this common assumption is false: a universally valid trade-offrelation between the noise and the disturbance has an additional correlationterm, which is redundant when the intervention brought by the measurement isindependent of the measured object, but which allows the noise-disturbanceproduct much below Planck's constant when the intervention is dependent. Amodel of measuring interaction with dependent intervention shows thatHeisenberg's lower bound for the noise-disturbance product is violated even bya nearly nondisturbing, precise position measuring instrument. An experimentalimplementation is also proposed to realize the above model in the context ofoptical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page

Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement