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arXiv:2602.18177

Experimental realization of a photonic weighted graph state for quantum metrology

Unathi Skosana, Byron Alexander, Changhyoup Lee, Mark Tame

quant-phSubmitted Feb 20, 2026• Announced Feb 23, 2026• 0 citations
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Abstract

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.

Comments
11 pages, 8 figures, appendix

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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.
Quantum metrology exploits quantum mechanical effects to increase the precision of measurements of physical quantities. A wide variety of applications are currently being developed for scientific and technological purposes, however, most research relies on the use of highly entangled resource states that are challenging to generate and control in a given physical system. Here, we study the use of weighted graph states as more accessible resources for quantum metrology, which yield a favorable precision beyond the classical limit, approaching the Heisenberg limit. We find a notable robustness to variation in weights and less challenging weight requirements compared to standard graph states, which require a maximal weight at all edges. Both of these aspects reduce the practical demands in a physical setup, with the latter implying significantly less entanglement is required to gain a quantum advantage in metrology. We study the quantum Fisher information and optimized estimator variance of two identified sub classes of weighted graph states for an arbitrary number of N qubits, providing analytical forms and investigating their scaling. Our work opens up opportunities for using weakly entangled states in quantum-enhanced metrology.
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Weighted graph states are a natural generalization of graph states, which are generated by applying controlled-phase gates, instead of controlled-Z gates, to a separable state. In this paper, we show that uniformly weighted graph states on a suitable planar graph constitute universal resources for measurement-based quantum computation for an arbitrary nonzero constant weight. To our knowledge, this is the first example of universal resources prepared with only non-maximally entangling gates and has potential applications to weakly interacting systems, such as photonic systems.
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