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Distributed quantum metrology can enhance the sensitivity for sensingspatially distributed parameters beyond the classical limits. Here wedemonstrate distributed quantum phase estimation with discrete variables toachieve Heisenberg limit phase measurements. Based on parallel entanglement inmodes and particles, we demonstrate distributed quantum sensing for bothindividual phase shifts and an averaged phase shift, with an error reduction upto 1.4 dB and 2.7 dB below the shot-noise limit. Furthermore, we demonstrate acombined strategy with parallel mode entanglement and multiple passes of thephase shifter in each mode. In particular, our experiment uses six entangledphotons with each photon passing the phase shifter up to six times, andachieves a total number of photon passes N=21 at an error reduction up to 4.7dB below the shot-noise limit. Our research provides a faithful verification ofthe benefit of entanglement and coherence for distributed quantum sensing ingeneral quantum networks.

Distributed quantum phase estimation with entangled photons