The change of a quantum state can generally only be fully monitored through simultaneous measurements of two non-commuting observables \(\hat{X}\) and \(\hat{Y}\) spanning a phase space. A measurement device that is coupled to the thermal environment provides at a time a pair of values that have a minimal uncertainty product set by the Heisenberg uncertainty relation, which limits the precision of the monitoring. Here, we report on an optical ensemble measurement setup that is able to monitor the time-dependent change of the quantum state’s displacement in phase space (\(\langle \hat{X}(t)\rangle ;\langle \hat{Y}(t)\rangle\)) with an imprecision 10 dB below the Heisenberg uncertainty limit. Our setup provides pairs of values (X(t_i); Y(t_i)) from simultaneous measurements at subsequent times t_i. The measurement references are not coupled to the thermal environment but are established by an entangled quantum state. Our achievement of a tenfold reduced quantum imprecision in monitoring arbitrary time-dependent displacements supports the potential of the quantum technology required for entanglement-enhanced metrology and sensing as well as measurement-based quantum computing.

量子态的变化通常只能通过同时测量跨越相空间的两个非交换可观测值\(\hat{X}\)和\(\hat{Y}\)来完全监测。与热环境耦合的测量设备一次提供一对值，这些值具有由海森堡不确定度关系设置的最小不确定度乘积，这限制了监测的精度。在这里，我们报告了一种光学系综测量装置，该装置能够监测相空间中量子态位移的时间相关变化（\(\langle \hat{X}(t)\rangle ;\langle \hat{Y }(t)\rangle\) ) 的精度低于海森堡不确定性极限 10 dB。我们的设置提供了成对的值 ( X (Ť_我）; Y ( t _i )) 来自后续时间t _{i 的}同时测量。测量参考不与热环境耦合，而是由纠缠量子态建立。我们在监测任意时间相关位移方面将量子不精确性降低了十倍，这支持了纠缠增强计量和传感以及基于测量的量子计算所需的量子技术的潜力。