Experimental realization of a photonic weighted graph state for quantum metrology

Quantum metrology seeks to push the boundaries of measurement precision by harnessing quantum phenomena. Conventional methods often rely on maximally entangled resources, with states that are usually challenging to produce and sustain in practical setups. Here, we show that the maximally entangled constraint can be lifted by experimentally realizing a photonic two-qubit weighted graph state with an arbitrarily tunable graph weight. We use the generated state as a resource for quantum-enhanced phase sensing. We experimentally characterize the state and study its minimum estimator variance for two distinct local measurement bases as the graph weight varies from the maximally entangled to weakly entangled limit. We find excellent quantitative agreement with theoretical predictions, and observe a gain in precision beyond the classically attainable precision limit for graph weights substantially below the maximally entangled limit. This confirms that considerably less entanglement is required to achieve a quantum advantage. Albeit non-scalable in our test setup, this work represents the first experimental realization of weighted graph states with a tunable graph weight using linear optics. We expect more scalable versions of the model to be possible in an on-chip photonic platform.