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

## TL;DR

This paper experimentally tests the error-tradeoff uncertainty relation using continuous-variable entangled states, confirming violations of Heisenberg's relation in some cases while validating Ozawa's and Brainciard's relations.

## Contribution

The study provides the first experimental verification of the error-tradeoff relation with continuous-variable EPR states, including cases with errors and mixed states.

## Key findings

- Heisenberg's error-tradeoff relation can be violated in continuous-variable systems.
- Ozawa's and Brainciard's relations remain valid where Heisenberg's is violated.
- Error-free measurement of one observable is experimentally verified.

## 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 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.