Optimal Generators for Quantum Sensing

We propose a computationally efficient method to derive the optimal unitary evolution under which a quantum state is most sensitive. This allows us to determine the optimal use of an entangled state for quantum sensing, even in complex systems where intuition from canonical squeezing examples breaks down. We use quantum state geometry to show that the maximal obtainable sensitivity using a given state is determined by the largest eigenvalue of the quantum Fisher information matrix (QFIM) and the corresponding evolution is uniquely determined by the coinciding eigenvector (Reilly, Wilson et al., Phys. Rev. Lett. 131, 150802). Since we optimize the process of parameter encoding rather than focusing on state preparation protocols, our scheme is relevant for any quantum sensor and may benefit all existing state preparation. This procedure naturally optimizes multiparameter estimation by determining, through the eigenvectors of the QFIM, the largest set of all possible commuting measurements with the best possible collective sensitivity.