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Phase measurement constitutes a key task in many fields of science, both inthe classical and quantum regime. The higher precision of such measurementoffers significant advances, and can also be utilised to achieve finerestimates for quantities such as distance, the gravitational constant,electromagnetic field amplitude, etc. Here we theoretically model the use of aquantum network, composed of a randomly coupled set of two-level systems, as aprocessing device for phase measurement. An incoming resource state carryingthe phase information interacts with the quantum network, whose emission istrained to produce a desired output signal. We demonstrate phase precisionscaling following the standard quantum limit, the Heisenberg limit, and beyond.This can be achieved using quantum resource states such as NOON states or otherentangled states, however, we also find that classically correlated mixtures ofstates are alone sufficient, provided that they exhibit quantum coherence. Ourproposed setup does not require conditional measurements, and is compatiblewith many different types of coupling between the quantum network and the phaseencoding state, hence making it attractive to a wide range of possible physicalimplementations.

Beating the classical phase precision limit using a quantum neuromorphic platform