Enhanced Quantum Metrology by Criticality-Assisted Noncommutative Preparation

Quantum criticality is a resource for quantum-enhanced metrology, but existing schemes face intrinsic limitations. These arise because using criticality directly in the encoding dynamics restricts the accessible parameters to those explicitly supported by the critical Hamiltonian, and the requirement for critical conditions narrows the effective estimation range. To solve this, we introduce a general framework termed criticality-assisted noncommutative preparation (CANP). In this approach, critical evolution is employed as a state-preparation resource. We establish the underlying algebraic conditions and show that the intrinsic noncommutativity between the preparation and encoding operations leads to a genuine enhancement of the quantum Fisher information (QFI). Remarkably, this enhancement may be achieved at fixed total sensing time and energy cost. The effect is quantified by the Wigner-Yanase skew information, which measures noncommutativity and exhibits the same critical scaling as the QFI. We demonstrate effective use of CANP in the quantum Rabi and Lipkin-Meshkov-Glick models. Our results establish CANP as a robust technique to effectively implement criticality-enhanced quantum metrology.