  In recent years, distributed quantum sensing has gained interest for a range
of applications requiring networks of sensors, from global-scale clock
synchronization to high energy physics. In particular, a network of entangled
sensors can improve not only the sensitivity beyond the shot noise limit, but
also enable a Heisenberg scaling with the number of sensors. Here, using bright
entangled twin beams, we theoretically and experimentally demonstrate the
detection of a linear combination of two distributed phases beyond the shot
noise limit with a truncated SU(1,1) interferometer. We experimentally
demonstrate a quantum noise reduction of 1.7 dB and a classical 3 dB
signal-to-noise ratio improvement over the separable sensing approach involving
two truncated SU(1,1) interferometers. Additionally, we theoretically extend
the use of a truncated SU(1,1) interferometer to a multi-phase-distributed
sensing scheme that leverages entanglement as a resource to achieve a quantum
improvement in the scaling with the number of sensors in the network. Our
results pave the way for developing quantum enhanced sensor networks that can
achieve an entanglement-enhanced sensitivity.
