Weighted graph states as a resource for quantum metrology

TL;DR

This paper investigates weighted graph states as practical and robust quantum resources for enhanced metrology, achieving precision beyond classical limits with less entanglement and control complexity.

Contribution

It introduces weighted graph states as accessible alternatives to highly entangled states for quantum metrology, with analytical results on their quantum Fisher information and scaling.

Findings

Weighted graph states surpass classical measurement limits.

Less entanglement is needed compared to standard graph states.

Robustness to weight variations enhances practical feasibility.

Abstract

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.