# Experimental test of error-disturbance uncertainty relation with continuous variables

## TL;DR

This paper experimentally tests the error-disturbance uncertainty relation for continuous variables in quantum mechanics, verifying the violation of Heisenberg's relation while confirming Ozawa's and Branciard's formulations using optical Gaussian states.

## Contribution

First experimental verification of error-disturbance uncertainty relations for continuous variables in quantum optics, demonstrating violations of Heisenberg's relation and validation of alternative formulations.

## Key findings

- Heisenberg's EDR is violated in the experiment.
- Ozawa's and Branciard's EDR are validated for continuous variables.
- Experimental setup uses heterodyne measurement on optical Gaussian states.

## Abstract

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.