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 errordisturbance uncertainty relation can be violated in some cases. We experimentally test the errortradeoff 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 errortradeoff 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.I.

Linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state

“…The rest two equations, Eqs. ( 27) and (28), are essential for understanding the performance of X ν , Y 2 ν , Y 0 ν and Z ν . From Eq.…”

“…Above all, the theory of uncertainty relations [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], the central topic of the paper, has advanced dramatically in the last two decades. Experimental tests of uncertainty relations [20][21][22][23][24][25][26][27][28][29] also have been performed due to the rapid improvement of experimental techniques in recent years. In the paper, we present linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state.…”

Experimental demonstration of robustness of Gaussian quantum coherence

“…Gaussian states, such as the squeezed state and the Einstein-Podolsky-Rosen (EPR) entangled state, play essential roles in continu-ous variable (CV) quantum information [29][30][31], where Gaussian states are generated deterministically and information is encoded in the position or momentum quadrature of photonic harmonic oscillators. For example, Gaussian states has been applied in quantum computation [32,33], quantum key distribution [34][35][36], quantum teleportation [37,38], quantum entanglement swapping [39][40][41], quantum dense coding [42,43], and verification of the error-disturbance uncertainty relation [44,45]. Recently, it has been shown that quantum coherence with infinite-dimensional systems can be quantified by relative entropy [46].…”

Experimental test of error-disturbance uncertainty relation with continuous variables

“…All of these experiments are in discrete-variable systems. Until recently, the test of the error-tradeoff uncertainty relation with continuous variables is experimentally demonstrated by using an Einstein-Podolsky-Rosen (EPR) entangled state [35].…”