  Uncertainty relation is one of the fundamental principle in quantum mechanics
and plays an important role in quantum information science. We experimentally
test the error-disturbance uncertainty relation (EDR) with continuous variables
for Gaussian states. Two conjugate continuous-variable observables, amplitude
and phase quadratures of an optical mode, are measured simultaneously by using
a heterodyne measurement system. The EDR with continuous variables for a
coherent state, a squeezed state and a thermal state are verified
experimentally. Our experimental results demonstrate that Heisenberg's EDR with
continuous variables is violated, yet Ozawa's and Branciard's EDR with
continuous variables are validated.
