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.

中文翻译：

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连续变量误差-干扰不确定关系的实验检验

不确定性关系是量子力学的基本原理之一，在量子信息科学中占有重要地位。我们用高斯状态的连续变量通过实验测试误差-干扰不确定性关系 (EDR)。使用外差测量系统同时测量两个共轭连续变量观测值，即光模的振幅和相位正交。实验验证了具有相干状态、压缩状态和热状态的连续变量的 EDR。我们的实验结果表明，连续变量的 Heisenberg 的 EDR 被违反，但 Ozawa 和 Branciard 的连续变量的 EDR 得到了验证。