Experimental test of error-tradeoff uncertainty relation using a continuous-variable entangled state

Abstract

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 is not valid in some cases. We experimentally test the error-tradeoff uncertainty relation by using a continuous-variable Gaussian 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 relation is violated in some cases for a continuous-variable system, while the Ozawa’s and Branciard’s relations are valid.