We unify the equilibrium and dynamic sensing frameworks of quantum metrology within the context of many-body systems. We investigate dynamic sensing schemes to derive an upper bound on the quantum Fisher information for probe states in thermal equilibrium with their environment. By identifying that the operator seminorm can be a robust measure of noncommutativity for finite-dimensional quantum systems, we establish that the dynamic quantum Fisher information for a thermal probe state is upper bounded by the degree of noncommutation between the transformed local generator and the Hamiltonian for the thermal state. Furthermore, we show that this upper bound scales as the square of the product of the inverse temperature and the evolution time. We establish an additional upper bound expressed in terms of the variance (or seminorm) of the commutator divided by the minimum nonzero energy gap, which proves particularly useful in the low-temperature regime and remains applicable to Hamiltonians with degenerate energy spectra. We apply this thermal dynamic sensing scheme to various quantum many-spin models, demonstrating that the dynamic quantum Fisher information satisfies the established upper bounds. In particular, we show that the variance-based bound remains valid for thermal dynamic sensing protocols in infinite-dimensional systems.

Close

PrevNext

View figure in article

• Quantum Fisher information
• Quantum metrology
• Quantum parameter estimation
• Quantum sensing