Quantum sensing with critical systems: advantages and challenges

Entangled states are a key resource for quantum sensing, enabling highly precise measurements of physical quantities such as magnetic fields. Common examples include Greenberger--Horne--Zeilinger (GHZ) states, squeezed states, and quantum critical states. We compare the strengths and weaknesses of using many-body critical states for interferometric quantum sensing relative to other types of entangled probes. We first identify the optimal measurement strategies for exploiting the advantages of critical states and relate these strategies to the system's internal and spatial symmetries. We then examine whether these advantages persist in realistic noisy environments, including local and global decoherence, bit-flip errors, qubit loss, and corruption by partial measurements. By systematically comparing critical states with GHZ states, we show that critical systems can, on average, outperform GHZ states under these noisy conditions. Importantly, we also find that when a critical state is partially measured and decoded, it can in certain cases exhibit an improved quantum Fisher information compared to the unmeasured state--revealing a new strategy improved quantum sensing.