Distributed quantum metrology can enhance the sensitivity for sensing spatially distributed parameters beyond the classical limits. Here we demonstrate distributed quantum phase estimation with discrete variables to achieve Heisenberg limit phase measurements. Based on parallel entanglement in modes and particles, we demonstrate distributed quantum sensing for both individual phase shifts and an averaged phase shift, with an error reduction up to 1.4 dB and 2.7 dB below the shot-noise limit. Furthermore, we demonstrate a combined strategy with parallel mode entanglement and multiple passes of the phase shifter in each mode. In particular, our experiment uses six entangled photons with each photon passing the phase shifter up to six times, and achieves a total number of photon passes N = 21 at an error reduction up to 4.7 dB below the shot-noise limit. Our research provides a faithful verification of the benefit of entanglement and coherence for distributed quantum sensing in general quantum networks.

分布式量子计量可以提高检测超出经典限制的空间分布参数的灵敏度。在这里，我们展示了具有离散变量的分布式量子相位估计，以实现海森堡极限相位测量。基于模式和粒子中的并行纠缠，我们展示了针对单个相移和平均相移的分布式量子感测，其误差减小到散粒噪声极限以下分别高达1.4 dB和2.7 dB。此外，我们展示了一种具有并行模式纠缠和每种模式下移相器多次通过的组合策略。尤其是，我们的实验使用了六个纠缠光子，每个光子通过移相器的次数最多为六次，从而获得了总数为N的光子通过 = 21，在低于散粒噪声限制的4.7 dB处减少了误差。我们的研究为常规量子网络中分布式量子传感纠缠和相干的好处提供了忠实的验证。