Linear quantum measurements with independent particles are bounded by the standard quantum limit, which limits the precision achievable in estimating unknown phase parameters. The standard quantum limit can be overcome by entangling the particles, but the sensitivity is often limited by the final state readout, especially for complex entangled many-body states with non-Gaussian probability distributions. Here, by implementing an effective time-reversal protocol in an optically engineered many-body spin Hamiltonian, we demonstrate a quantum measurement with non-Gaussian states with performance beyond the limit of the readout scheme. This signal amplification through a time-reversed interaction achieves the greatest phase sensitivity improvement beyond the standard quantum limit demonstrated to date in any full Ramsey interferometer. These results open the field of robust time-reversal-based measurement protocols offering precision not too far from the Heisenberg limit. Potential applications include quantum sensors that operate at finite bandwidth, and the principle we demonstrate may also advance areas such as quantum engineering, quantum measurements and the search for new physics using optical-transition atomic clocks.

具有独立粒子的线性量子测量受标准量子极限的限制，这限制了在估计未知相位参数时可达到的精度。标准量子极限可以通过粒子纠缠来克服，但灵敏度通常受到最终状态读数的限制，特别是对于具有非高斯概率分布的复杂纠缠多体状态。在这里，通过在光学设计的多体自旋哈密顿量中实现有效的时间反转协议，我们展示了具有非高斯状态的量子测量，其性能超出了读出方案的限制。这种通过时间反转相互作用的信号放大实现了最大的相位灵敏度改进，超出了迄今为止在任何完整的拉姆齐干涉仪中展示的标准量子极限。这些结果打开了稳健的基于时间反转的测量协议的领域，提供的精度与海森堡极限相差不远。潜在的应用包括在有限带宽下运行的量子传感器，我们展示的原理还可能推进量子工程、量子测量和使用光学跃迁原子钟寻找新物理等领域。