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

Yang Liu,Zhihao Ma,Xiaolong Su,Kunchi Peng,Meihong Wang,Zhongzhong Qin,Dongmei Han,Haijun Kang

doi:10.1038/s41534-019-0183-6

Yang Liu, Zhihao Ma + Show 6 more

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https://doi.org/10.1038/s41534-019-0183-6

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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.

Highlights

As one of the cornerstones of quantum mechanics, uncertainty relation describes the measurement limitation on two incompatible observables.[1]
A Gaussian EPR entangled state is used in the experimental test of error–tradeoff uncertainty relations with continuous variables
It is important to show that the error–tradeoff relation can be saturated, i.e., the lower bound of error–tradeoff relation can be reached

Summary

Introduction

As one of the cornerstones of quantum mechanics, uncertainty relation describes the measurement limitation on two incompatible observables.[1]. While in the original spirit of Heisenberg’s idea,[1] the Heisenberg’s uncertainty principle should be based on the observer’s effect, which means that measurement of a certain system cannot be made without affecting the system. This leads to the second type of uncertainty relation: measurement uncertainty relation, which studies to what extent the accuracy of position measurement of a particle is related to the disturbance of the particle’s momentum, so called the error–disturbance uncertainty relation.[11,12] It is called the error–tradeoff relation in the approximate joint measurements of two incompatible observables.[13,14]

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