Anti-Critical Quantum Metrology

Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. Traditionally, this enhancement is associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. Consequently, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down, rather than a genuine gain in metrological performance, thereby severely limiting the practical usefulness of such protocols. Here we show that the relationship between energy-gap variations, quantum Fisher information, and achievable precision is far more subtle in interacting quantum systems: enhanced sensitivity does not require a vanishing gap, and, perhaps more surprisingly, a decreasing quantum Fisher information does not necessarily imply reduced precision once the time is properly taken into account. Building on this insight, we introduce an anti-critical metrology scheme that achieves enhanced precision while the energy gap increases. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the critical slowing down associated with conventional criticality.