Distributed quantum phase estimation with entangled photons

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. Distributed quantum metrology is demonstrated for both individual and averaged phase shifts by using discrete-variable entangled photons. An error reduction of 4.7 dB below the shot-noise limit is achieved when a total number of photon passes is 21.