  Heisenberg formulated a noise-disturbance principle stating that there is a
tradeoff between noise and disturbance when a measurement of position and a
measurement of momentum are performed sequentially, and another principle
imposing a limitation on the product of the uncertainties in a joint
measurement of position and momentum. We prove that the former, the Heisenberg
sequential noise-disturbance principle, holds when the detectors are assumed to
be initially uncorrelated from each other, but that it can be violated for some
properly correlated initial preparations of the detectors.
