  Ozawa's measurement-disturbance relation is generalized to a phase-space
noncommutative extension of quantum mechanics. It is shown that the
measurement-disturbance relations have additional terms for backaction evading
quadrature amplifiers and for noiseless quadrature transducers. Several
distinctive features appear as a consequence of the noncommutative extension:
measurement interactions which are noiseless, and observables which are
undisturbed by a measurement, or of independent intervention in ordinary
quantum mechanics, may acquire noise, become disturbed by the measurement, or
no longer be an independent intervention in noncommutative quantum mechanics.
It is also found that there can be states which violate Ozawa's universal
noise-disturbance trade-off relation, but verify its noncommutative
deformation.
