Quantum metrology explores the benefits of quantum coherence and entanglement for making precision measurements. Recently there has been growing interest in understanding how quantum metrological techniques can be used to enhance measurements that are spatially distributed. In this talk I will first introduce the idea of distributed quantum metrology, then I will discuss the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state. I will show that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology. Conversely, I will show that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer.
