  Heisenberg's original uncertainty relation is related to measurement effect,
which is different from the preparation uncertainty relation. However, it has
been shown that Heisenberg's error-disturbance uncertainty relation can be
violated in some cases. We experimentally test the error-tradeoff uncertainty
relation by using a continuous-variable Einstein-Podolsky-Rosen (EPR) entangled
state. Based on the quantum correlation between the two entangled optical
beams, the errors on amplitude and phase quadratures of one EPR optical beam
coming from joint measurement are estimated respectively, which are used to
verify the error-tradeoff relation. Especially, the error-tradeoff relation for
error-free measurement of one observable is verified in our experiment. We also
verify the error-tradeoff relations for nonzero errors and mixed state by
introducing loss on one EPR beam. Our experimental results demonstrate that
Heisenberg's error-tradeoff uncertainty relation is violated in some cases for
a continuous-variable system, while the Ozawa's and Brainciard's relations are
valid.
